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Theorem feq23d 6664
Description: Equality deduction for functions. (Contributed by NM, 8-Jun-2013.)
Hypotheses
Ref Expression
feq23d.1 (𝜑𝐴 = 𝐶)
feq23d.2 (𝜑𝐵 = 𝐷)
Assertion
Ref Expression
feq23d (𝜑 → (𝐹:𝐴𝐵𝐹:𝐶𝐷))

Proof of Theorem feq23d
StepHypRef Expression
1 eqidd 2734 . 2 (𝜑𝐹 = 𝐹)
2 feq23d.1 . 2 (𝜑𝐴 = 𝐶)
3 feq23d.2 . 2 (𝜑𝐵 = 𝐷)
41, 2, 3feq123d 6658 1 (𝜑 → (𝐹:𝐴𝐵𝐹:𝐶𝐷))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205   = wceq 1542  wf 6493
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-rab 3407  df-v 3446  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-sn 4588  df-pr 4590  df-op 4594  df-br 5107  df-opab 5169  df-rel 5641  df-cnv 5642  df-co 5643  df-dm 5644  df-rn 5645  df-fun 6499  df-fn 6500  df-f 6501
This theorem is referenced by:  nvof1o  7227  axdc4uz  13895  isacs  17536  isfunc  17755  funcres  17787  funcpropd  17792  estrcco  18022  funcestrcsetclem9  18041  fullestrcsetc  18044  fullsetcestrc  18059  1stfcl  18090  2ndfcl  18091  evlfcl  18116  curf1cl  18122  yonedalem3b  18173  intopsn  18514  mhmpropd  18613  pwssplit1  20535  islindf  21234  evls1sca  21705  rrxds  24773  wlkp1  28671  acunirnmpt  31621  fnpreimac  31633  pwrssmgc  31909  cnmbfm  32920  elmrsubrn  34171  poimirlem3  36127  poimirlem28  36152  isrngod  36403  rngosn3  36429  isgrpda  36460  islfld  37570  tendofset  39267  tendoset  39268  mapfzcons  41082  diophrw  41125  refsum2cnlem1  43330  mgmhmpropd  46165  funcringcsetcALTV2lem9  46428  funcringcsetclem9ALTV  46451  aacllem  47334
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