Theorem feq2i 5504

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 5494	. 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 5350

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 2216

This theorem depends on definitions:  df-bi 117  df-cleq 2227  df-fn 5357  df-f 5358

This theorem is referenced by:  fmpox  6398  fmpo  6399  tposf  6505  issmo  6521  tfrcllemsucfn  6586  1fv  10477  fxnn0nninf  10805  snopiswrd  11238  iswrddm0  11252  0met  15266  dvef  15609  uhgr0e  16094  vtxdumgrfival  16310  gfsum0  16881