Theorem feq23i 5041

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 5033	. 2 |- ( ( A = C /\ B = D ) -> ( F : A --> B <-> F : C --> D ) )
4	1, 2, 3	mp2an 402	1 |- ( F : A --> B <-> F : C --> D )

Syntax hints:   <-> wb 98   = wceq 1243   -->wf 4898

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-in 2924  df-ss 2931  df-fn 4905  df-f 4906

This theorem is referenced by:  ftpg  5347