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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 )