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Theorem feq23d 5386
Description: Equality deduction for functions. (Contributed by NM, 8-Jun-2013.)
Hypotheses
Ref Expression
feq23d.1  |-  ( ph  ->  A  =  C )
feq23d.2  |-  ( ph  ->  B  =  D )
Assertion
Ref Expression
feq23d  |-  ( ph  ->  ( F : A --> B 
<->  F : C --> D ) )

Proof of Theorem feq23d
StepHypRef Expression
1 eqidd 2284 . 2  |-  ( ph  ->  F  =  F )
2 feq23d.1 . 2  |-  ( ph  ->  A  =  C )
3 feq23d.2 . 2  |-  ( ph  ->  B  =  D )
41, 2, 3feq123d 5382 1  |-  ( ph  ->  ( F : A --> B 
<->  F : C --> D ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176    = wceq 1623   -->wf 5251
This theorem is referenced by:  axdc4uz  11045  isacs  13553  isfunc  13738  funcres  13770  funcpropd  13774  funcres2c  13775  catciso  13939  1stfcl  13971  2ndfcl  13972  evlfcl  13996  curf1cl  14002  yonedalem4c  14051  yonedalem3b  14053  yonedainv  14055  mhmpropd  14421  iscau  18702  isgrp2d  20902  isgrpda  20964  isrngo  21045  isrngod  21046  rngosn3  21093  ajfval  21387  cnmbfm  23568  orvcval4  23661  vecval1b  25451  vecval3b  25452  tcnvec  25690  setiscat  25979  mapfzcons  26793  diophrw  26838  pwssplit1  27188  islindf  27282  refsum2cnlem1  27708  islfld  29252  tendofset  30947  tendoset  30948
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-rn 4700  df-fun 5257  df-fn 5258  df-f 5259
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