Theorem feq2i 5439

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 5429	. 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 1373   -->wf 5286

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 1471  ax-gen 1473  ax-4 1534  ax-17 1550  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-cleq 2200  df-fn 5293  df-f 5294

This theorem is referenced by:  fmpox  6309  fmpo  6310  tposf  6381  issmo  6397  tfrcllemsucfn  6462  1fv  10296  fxnn0nninf  10621  snopiswrd  11041  iswrddm0  11055  0met  14971  dvef  15314  uhgr0e  15793