Metamath Proof Explorer


Theorem xrneq2d

Description: Equality theorem for the range Cartesian product, deduction form. (Contributed by Peter Mazsa, 7-Sep-2021)

Ref Expression
Hypothesis xrneq2d.1 ( 𝜑𝐴 = 𝐵 )
Assertion xrneq2d ( 𝜑 → ( 𝐶𝐴 ) = ( 𝐶𝐵 ) )

Proof

Step Hyp Ref Expression
1 xrneq2d.1 ( 𝜑𝐴 = 𝐵 )
2 xrneq2 ( 𝐴 = 𝐵 → ( 𝐶𝐴 ) = ( 𝐶𝐵 ) )
3 1 2 syl ( 𝜑 → ( 𝐶𝐴 ) = ( 𝐶𝐵 ) )