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Theorem feq23d 6713
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 6707 1 (𝜑 → (𝐹:𝐴𝐵𝐹:𝐶𝐷))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205   = wceq 1542  wf 6540
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 3434  df-v 3477  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4324  df-if 4530  df-sn 4630  df-pr 4632  df-op 4636  df-br 5150  df-opab 5212  df-rel 5684  df-cnv 5685  df-co 5686  df-dm 5687  df-rn 5688  df-fun 6546  df-fn 6547  df-f 6548
This theorem is referenced by:  nvof1o  7278  axdc4uz  13949  isacs  17595  isfunc  17814  funcres  17846  funcpropd  17851  estrcco  18081  funcestrcsetclem9  18100  fullestrcsetc  18103  fullsetcestrc  18118  1stfcl  18149  2ndfcl  18150  evlfcl  18175  curf1cl  18181  yonedalem3b  18232  intopsn  18573  mhmpropd  18678  pwssplit1  20670  islindf  21367  evls1sca  21842  rrxds  24910  wlkp1  28938  acunirnmpt  31884  fnpreimac  31896  pwrssmgc  32170  cnmbfm  33262  elmrsubrn  34511  poimirlem3  36491  poimirlem28  36516  isrngod  36766  rngosn3  36792  isgrpda  36823  islfld  37932  tendofset  39629  tendoset  39630  mapfzcons  41454  diophrw  41497  refsum2cnlem1  43721  mgmhmpropd  46555  funcringcsetcALTV2lem9  46942  funcringcsetclem9ALTV  46965  aacllem  47848
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