Theorem feq23i 6039

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 6029	. 2 |- ( ( A = C /\ B = D ) -> ( F : A --> B <-> F : C --> D ) )
4	1, 2, 3	mp2an 708	1 |- ( F : A --> B <-> F : C --> D )

Syntax hints:   <-> wb 196   = wceq 1483   -->wf 5884

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-in 3581  df-ss 3588  df-fn 5891  df-f 5892

This theorem is referenced by:  ftpg  6423  hashf  13125  funcoppc  16535  cnextfval  21866  uhgr0  25968  lfgredgge2  26019  mbfmvolf  30328  eulerpartlemt  30433  ismgmOLD  33649  elghomOLD  33686  tendoset  36047  pwssplit4  37659  lincdifsn  42213