Theorem feq2i 5483

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 5473	. 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 1398   -->wf 5329

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 1496  ax-gen 1498  ax-4 1559  ax-17 1575  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-cleq 2224  df-fn 5336  df-f 5337

This theorem is referenced by:  fmpox  6374  fmpo  6375  tposf  6481  issmo  6497  tfrcllemsucfn  6562  1fv  10436  fxnn0nninf  10764  snopiswrd  11189  iswrddm0  11203  0met  15195  dvef  15538  uhgr0e  16023  vtxdumgrfival  16239  gfsum0  16811