Metamath Proof Explorer


Theorem imaeq2i

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

Ref Expression
Hypothesis imaeq1i.1
|- A = B
Assertion imaeq2i
|- ( C " A ) = ( C " B )

Proof

Step Hyp Ref Expression
1 imaeq1i.1
 |-  A = B
2 imaeq2
 |-  ( A = B -> ( C " A ) = ( C " B ) )
3 1 2 ax-mp
 |-  ( C " A ) = ( C " B )