Theorem feq2i 5530

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 5520	. 2 |- ( A = B -> ( F : A --> C <-> F : B --> C ) )
3	1, 2	ax-mp 5	1 |- ( F : A --> C <-> F : B --> C )

This proof depends on syntax axioms:   <-> wb 105   = wceq 1402   -->wf 5376

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-4 1563  ax-17 1579  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-cleq 2231  df-fn 5383  df-f 5384

This theorem is used by:  fmpox  6440  fmpo  6441  tposf  6547  issmo  6563  tfrcllemsucfn  6628  1fv  10563  fxnn0nninf  10897  snopiswrd  11336  iswrddm0  11350  gsum0cmn  14244  gsumsnfdcmn  14257  0met  15610  dvef  15953  uhgr0e  16528  vtxdumgrfival  16744