Theorem feq23i 5061

Description: Equality inference for functions. (Contributed by Paul Chapman, 22-Jun-2011.)

Hypotheses

Ref	Expression
feq23i.1	|- A = C
feq23i.2	|- B = D

Assertion

Ref	Expression
feq23i	|- ( F : A --> B <-> F : C --> D )

Proof of Theorem feq23i

Step	Hyp	Ref	Expression
1		feq23i.1	. 2 |- A = C
2		feq23i.2	. 2 |- B = D
3		feq23 5053	. 2 |- ( ( A = C /\ B = D ) -> ( F : A --> B <-> F : C --> D ) )
4	1, 2, 3	mp2an 416	1 |- ( F : A --> B <-> F : C --> D )

Syntax hints:   <-> wb 103   = wceq 1284   -->wf 4918

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-11 1437  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-in 2979  df-ss 2986  df-fn 4925  df-f 4926

This theorem is referenced by:  ftpg  5368