Metamath Proof Explorer


Theorem xrneq1i

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

Ref Expression
Hypothesis xrneq1i.1 ⊢ A = B
Assertion xrneq1i ⊢ A ⋉ C = B ⋉ C

Proof

Step Hyp Ref Expression
1 xrneq1i.1 ⊢ A = B
2 xrneq1 ⊢ A = B → A ⋉ C = B ⋉ C
3 1 2 ax-mp ⊢ A ⋉ C = B ⋉ C