Theorem feq2i 5476

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 5466	. 2 |- ( A = B -> ( F : A --> C <-> F : B --> C ) )
3	1, 2	ax-mp 5	1 |- ( F : A --> C <-> F : B --> C )

Syntax hints:   <-> wb 105   = wceq 1397   -->wf 5322

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1495  ax-gen 1497  ax-4 1558  ax-17 1574  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-cleq 2224  df-fn 5329  df-f 5330

This theorem is referenced by:  fmpox  6365  fmpo  6366  tposf  6438  issmo  6454  tfrcllemsucfn  6519  1fv  10374  fxnn0nninf  10702  snopiswrd  11127  iswrddm0  11141  0met  15127  dvef  15470  uhgr0e  15952  vtxdumgrfival  16168  gfsum0  16734