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Theorem feq23i 5401
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
StepHypRef Expression
1 feq23i.1 . 2  |-  A  =  C
2 feq23i.2 . 2  |-  B  =  D
3 feq23 5394 . 2  |-  ( ( A  =  C  /\  B  =  D )  ->  ( F : A --> B 
<->  F : C --> D ) )
41, 2, 3mp2an 653 1  |-  ( F : A --> B  <->  F : C
--> D )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    = wceq 1632   -->wf 5267
This theorem is referenced by:  funcoppc  13765  ismgm  21003  elghom  21046  mbfmvolf  23586  vecval1b  25554  pgapspf  26155  ftp  26996  pwssplit4  27294  wlkntrllem1  28345  wlkntrllem3  28347  tendoset  31570
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-in 3172  df-ss 3179  df-fn 5274  df-f 5275
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