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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 )