Theorem feq2i 5274

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 5264	. 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 104   = wceq 1332   -->wf 5127

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-4 1488  ax-17 1507  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-cleq 2133  df-fn 5134  df-f 5135

This theorem is referenced by:  fmpox  6106  fmpo  6107  tposf  6177  issmo  6193  tfrcllemsucfn  6258  1fv  9947  fxnn0nninf  10242  0met  12592  dvef  12896