Theorem feq2i 5060

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 5051	. 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 103   = wceq 1284   -->wf 4918

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-4 1440  ax-17 1459  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-cleq 2074  df-fn 4925  df-f 4926

This theorem is referenced by:  fmpt2x  5846  fmpt2  5847  tposf  5910  issmo  5926  1fv  9149  iseqf  9444