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
|- ( A " C ) = ( B " C )

Proof

Step Hyp Ref Expression
1 imaeq1i.1
 |-  A = B
2 imaeq1
 |-  ( A = B -> ( A " C ) = ( B " C ) )
3 1 2 ax-mp
 |-  ( A " C ) = ( B " C )