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Metamath Proof Explorer

Theorem xrneq2i

Description: Equality theorem for the range Cartesian product, inference form. (Contributed by Peter Mazsa, 16-Dec-2020)

Ref Expression
Hypothesis xrneq2i.1 ⊢ A = B
Assertion xrneq2i ⊢ C ⋉ A = C ⋉ B

Proof

Step Hyp Ref Expression
1 xrneq2i.1 ⊢ A = B
2 xrneq2 ⊢ A = B → C ⋉ A = C ⋉ B
3 1 2 ax-mp ⊢ C ⋉ A = C ⋉ B