Theorem feq2i 5155

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 5146	. 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 1289   -->wf 5011

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 1381  ax-gen 1383  ax-4 1445  ax-17 1464  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-cleq 2081  df-fn 5018  df-f 5019

This theorem is referenced by:  fmpt2x  5970  fmpt2  5971  tposf  6037  issmo  6053  tfrcllemsucfn  6118  1fv  9550  fxnn0nninf  9844  iseqfcl  9878