Theorem feq23 6029

Description: Equality theorem for functions. (Contributed by FL, 14-Jul-2007.) (Proof shortened by Andrew Salmon, 17-Sep-2011.)

Assertion

Ref	Expression
feq23	|- ( ( A = C /\ B = D ) -> ( F : A --> B <-> F : C --> D ) )

Proof of Theorem feq23

Step	Hyp	Ref	Expression
1		feq2 6027	. 2 |- ( A = C -> ( F : A --> B <-> F : C --> B ) )
2		feq3 6028	. 2 |- ( B = D -> ( F : C --> B <-> F : C --> D ) )
3	1, 2	sylan9bb 736	1 |- ( ( A = C /\ B = D ) -> ( F : A --> B <-> F : C --> D ) )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384   = 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:  feq23i  6039  ismgmOLD  33649  ismndo2  33673  rngomndo  33734  seff  38508