diff --git a/llvm/include/llvm/CodeGen/GlobalISel/CombinerHelper.h b/llvm/include/llvm/CodeGen/GlobalISel/CombinerHelper.h
--- a/llvm/include/llvm/CodeGen/GlobalISel/CombinerHelper.h
+++ b/llvm/include/llvm/CodeGen/GlobalISel/CombinerHelper.h
@@ -221,6 +221,10 @@
   /// equivalent instructions.
   bool matchEqualDefs(const MachineOperand &MOP1, const MachineOperand &MOP2);
 
+  /// Return true if \p MOP is defined by a G_CONSTANT with a value equal to
+  /// \p C.
+  bool matchConstantOp(const MachineOperand &MOP, int64_t C);
+
   /// Optimize (cond ? x : x) -> x
   bool matchSelectSameVal(MachineInstr &MI);
 
diff --git a/llvm/include/llvm/Target/GlobalISel/Combine.td b/llvm/include/llvm/Target/GlobalISel/Combine.td
--- a/llvm/include/llvm/Target/GlobalISel/Combine.td
+++ b/llvm/include/llvm/Target/GlobalISel/Combine.td
@@ -192,6 +192,14 @@
   (apply [{ return Helper.replaceSingleDefInstWithOperand(*${root}, 2); }])
 >;
 
+// Fold x op 0 -> x
+def right_identity_zero: GICombineRule<
+  (defs root:$root),
+  (match (wip_match_opcode G_SUB, G_ADD, G_OR, G_XOR, G_SHL, G_ASHR, G_LSHR):$root,
+    [{ return Helper.matchConstantOp(${root}->getOperand(2), 0); }]),
+  (apply [{ return Helper.replaceSingleDefInstWithOperand(*${root}, 1); }])
+>;
+
 // FIXME: These should use the custom predicate feature once it lands.
 def undef_combines : GICombineGroup<[undef_to_fp_zero, undef_to_int_zero,
                                      undef_to_negative_one,
@@ -199,7 +207,7 @@
                                      propagate_undef_all_ops,
                                      propagate_undef_shuffle_mask]>;
 
-def identity_combines : GICombineGroup<[select_same_val]>;
+def identity_combines : GICombineGroup<[select_same_val, right_identity_zero]>;
 
 def trivial_combines : GICombineGroup<[copy_prop, mul_to_shl]>;
 def all_combines : GICombineGroup<[trivial_combines, ptr_add_immed_chain,
diff --git a/llvm/lib/CodeGen/GlobalISel/CombinerHelper.cpp b/llvm/lib/CodeGen/GlobalISel/CombinerHelper.cpp
--- a/llvm/lib/CodeGen/GlobalISel/CombinerHelper.cpp
+++ b/llvm/lib/CodeGen/GlobalISel/CombinerHelper.cpp
@@ -9,6 +9,7 @@
 #include "llvm/CodeGen/GlobalISel/Combiner.h"
 #include "llvm/CodeGen/GlobalISel/GISelChangeObserver.h"
 #include "llvm/CodeGen/GlobalISel/GISelKnownBits.h"
+#include "llvm/CodeGen/GlobalISel/MIPatternMatch.h"
 #include "llvm/CodeGen/GlobalISel/MachineIRBuilder.h"
 #include "llvm/CodeGen/GlobalISel/Utils.h"
 #include "llvm/CodeGen/MachineDominators.h"
@@ -23,6 +24,7 @@
 #define DEBUG_TYPE "gi-combiner"
 
 using namespace llvm;
+using namespace MIPatternMatch;
 
 // Option to allow testing of the combiner while no targets know about indexed
 // addressing.
@@ -1546,6 +1548,13 @@
   return Builder.getTII().produceSameValue(*I1, *I2, &MRI);
 }
 
+bool CombinerHelper::matchConstantOp(const MachineOperand &MOP, int64_t C) {
+  if (!MOP.isReg())
+    return false;
+  int64_t Cst;
+  return mi_match(MOP.getReg(), MRI, m_ICst(Cst)) && Cst == C;
+}
+
 bool CombinerHelper::replaceSingleDefInstWithOperand(MachineInstr &MI,
                                                      unsigned OpIdx) {
   assert(MI.getNumExplicitDefs() == 1 && "Expected one explicit def?");
diff --git a/llvm/test/CodeGen/AArch64/GlobalISel/prelegalizercombiner-trivial-arith.mir b/llvm/test/CodeGen/AArch64/GlobalISel/prelegalizercombiner-trivial-arith.mir
new file mode 100644
--- /dev/null
+++ b/llvm/test/CodeGen/AArch64/GlobalISel/prelegalizercombiner-trivial-arith.mir
@@ -0,0 +1,163 @@
+# NOTE: Assertions have been autogenerated by utils/update_mir_test_checks.py
+# RUN: llc -mtriple aarch64 -run-pass=aarch64-prelegalizer-combiner -verify-machineinstrs %s -o - | FileCheck %s
+
+name:            right_ident_sub
+tracksRegLiveness: true
+body:             |
+  bb.1.entry:
+    liveins: $w0
+    ; Fold (x - 0) -> x
+    ;
+    ; CHECK-LABEL: name: right_ident_sub
+    ; CHECK: liveins: $w0
+    ; CHECK: %x:_(s32) = COPY $w0
+    ; CHECK: $w0 = COPY %x(s32)
+    ; CHECK: RET_ReallyLR implicit $w0
+    %x:_(s32) = COPY $w0
+    %cst:_(s32) = G_CONSTANT i32 0
+    %op:_(s32) = G_SUB %x(s32), %cst
+    $w0 = COPY %op(s32)
+    RET_ReallyLR implicit $w0
+
+...
+---
+name:            right_ident_add
+tracksRegLiveness: true
+body:             |
+  bb.1.entry:
+    liveins: $w0
+    ; Fold (x + 0) -> x
+    ;
+    ; CHECK-LABEL: name: right_ident_add
+    ; CHECK: liveins: $w0
+    ; CHECK: %x:_(s32) = COPY $w0
+    ; CHECK: $w0 = COPY %x(s32)
+    ; CHECK: RET_ReallyLR implicit $w0
+    %x:_(s32) = COPY $w0
+    %cst:_(s32) = G_CONSTANT i32 0
+    %op:_(s32) = G_ADD %x(s32), %cst
+    $w0 = COPY %op(s32)
+    RET_ReallyLR implicit $w0
+
+...
+---
+name:            right_ident_or
+tracksRegLiveness: true
+body:             |
+  bb.1.entry:
+    liveins: $w0
+    ; Fold (x || 0) -> x
+    ;
+    ; CHECK-LABEL: name: right_ident_or
+    ; CHECK: liveins: $w0
+    ; CHECK: %x:_(s32) = COPY $w0
+    ; CHECK: $w0 = COPY %x(s32)
+    ; CHECK: RET_ReallyLR implicit $w0
+    %x:_(s32) = COPY $w0
+    %cst:_(s32) = G_CONSTANT i32 0
+    %op:_(s32) = G_OR %x(s32), %cst
+    $w0 = COPY %op(s32)
+    RET_ReallyLR implicit $w0
+
+...
+---
+name:            right_ident_xor
+tracksRegLiveness: true
+body:             |
+  bb.1.entry:
+    liveins: $w0
+    ; Fold (x | 0) -> x
+    ;
+    ; CHECK-LABEL: name: right_ident_xor
+    ; CHECK: liveins: $w0
+    ; CHECK: %x:_(s32) = COPY $w0
+    ; CHECK: $w0 = COPY %x(s32)
+    ; CHECK: RET_ReallyLR implicit $w0
+    %x:_(s32) = COPY $w0
+    %cst:_(s32) = G_CONSTANT i32 0
+    %op:_(s32) = G_XOR %x(s32), %cst
+    $w0 = COPY %op(s32)
+    RET_ReallyLR implicit $w0
+
+...
+---
+name:            right_ident_shl
+tracksRegLiveness: true
+body:             |
+  bb.1.entry:
+    liveins: $w0
+    ; Fold (x << 0) -> x
+    ;
+    ; CHECK-LABEL: name: right_ident_shl
+    ; CHECK: liveins: $w0
+    ; CHECK: %x:_(s32) = COPY $w0
+    ; CHECK: $w0 = COPY %x(s32)
+    ; CHECK: RET_ReallyLR implicit $w0
+    %x:_(s32) = COPY $w0
+    %cst:_(s32) = G_CONSTANT i32 0
+    %op:_(s32) = G_SHL %x(s32), %cst
+    $w0 = COPY %op(s32)
+    RET_ReallyLR implicit $w0
+
+...
+---
+name:            right_ident_ashr
+tracksRegLiveness: true
+body:             |
+  bb.1.entry:
+    liveins: $w0
+    ; Fold (x ashr 0) -> x
+    ;
+    ; CHECK-LABEL: name: right_ident_ashr
+    ; CHECK: liveins: $w0
+    ; CHECK: %x:_(s32) = COPY $w0
+    ; CHECK: $w0 = COPY %x(s32)
+    ; CHECK: RET_ReallyLR implicit $w0
+    %x:_(s32) = COPY $w0
+    %cst:_(s32) = G_CONSTANT i32 0
+    %op:_(s32) = G_ASHR %x(s32), %cst
+    $w0 = COPY %op(s32)
+    RET_ReallyLR implicit $w0
+
+...
+---
+name:            right_ident_lshr
+tracksRegLiveness: true
+body:             |
+  bb.1.entry:
+    liveins: $w0
+    ; Fold (x lshr 0) -> x
+    ;
+    ; CHECK-LABEL: name: right_ident_lshr
+    ; CHECK: liveins: $w0
+    ; CHECK: %x:_(s32) = COPY $w0
+    ; CHECK: $w0 = COPY %x(s32)
+    ; CHECK: RET_ReallyLR implicit $w0
+    %x:_(s32) = COPY $w0
+    %cst:_(s32) = G_CONSTANT i32 0
+    %op:_(s32) = G_LSHR %x(s32), %cst
+    $w0 = COPY %op(s32)
+    RET_ReallyLR implicit $w0
+
+...
+---
+name:            dont_fold_sub
+tracksRegLiveness: true
+body:             |
+  bb.1.entry:
+    liveins: $w0
+    ; Not an identity, no folding.
+    ;
+    ; CHECK-LABEL: name: dont_fold_sub
+    ; CHECK: liveins: $w0
+    ; CHECK: %x:_(s32) = COPY $w0
+    ; CHECK: %cst:_(s32) = G_CONSTANT i32 1
+    ; CHECK: %op:_(s32) = G_SUB %x, %cst
+    ; CHECK: $w0 = COPY %op(s32)
+    ; CHECK: RET_ReallyLR implicit $w0
+    %x:_(s32) = COPY $w0
+    %cst:_(s32) = G_CONSTANT i32 1
+    %op:_(s32) = G_SUB %x(s32), %cst
+    $w0 = COPY %op(s32)
+    RET_ReallyLR implicit $w0
+...