Metamath Proof Explorer


Theorem imaeq1i

Description: Equality theorem for image. (Contributed by NM, 21-Dec-2008)

Ref Expression
Hypothesis imaeq1i.1 𝐴 = 𝐵
Assertion imaeq1i ( 𝐴𝐶 ) = ( 𝐵𝐶 )

Proof

Step Hyp Ref Expression
1 imaeq1i.1 𝐴 = 𝐵
2 imaeq1 ( 𝐴 = 𝐵 → ( 𝐴𝐶 ) = ( 𝐵𝐶 ) )
3 1 2 ax-mp ( 𝐴𝐶 ) = ( 𝐵𝐶 )