Theorem feq2i 5040

Description: Equality inference for functions. (Contributed by NM, 5-Sep-2011.)

Hypothesis

Ref	Expression
feq2i.1	|- A = B

Assertion

Ref	Expression
feq2i	|- ( F : A --> C <-> F : B --> C )

Proof of Theorem feq2i

Step	Hyp	Ref	Expression
1		feq2i.1	. 2 |- A = B
2		feq2 5031	. 2 |- ( A = B -> ( F : A --> C <-> F : B --> C ) )
3	1, 2	ax-mp 7	1 |- ( F : A --> C <-> F : B --> C )

Syntax hints:   <-> wb 98   = wceq 1243   -->wf 4898

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-4 1400  ax-17 1419  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-fn 4905  df-f 4906

This theorem is referenced by:  fmpt2x  5826  fmpt2  5827  tposf  5887  issmo  5903  1fv  8996  iseqf  9224