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Theorem feq23d 6078
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 2652 . 2 (𝜑𝐹 = 𝐹)
2 feq23d.1 . 2 (𝜑𝐴 = 𝐶)
3 feq23d.2 . 2 (𝜑𝐵 = 𝐷)
41, 2, 3feq123d 6072 1 (𝜑 → (𝐹:𝐴𝐵𝐹:𝐶𝐷))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196   = wceq 1523  wf 5922
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-rab 2950  df-v 3233  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-nul 3949  df-if 4120  df-sn 4211  df-pr 4213  df-op 4217  df-br 4686  df-opab 4746  df-rel 5150  df-cnv 5151  df-co 5152  df-dm 5153  df-rn 5154  df-fun 5928  df-fn 5929  df-f 5930
This theorem is referenced by:  nvof1o  6576  axdc4uz  12823  isacs  16359  isfunc  16571  funcres  16603  funcpropd  16607  estrcco  16817  funcestrcsetclem9  16835  fullestrcsetc  16838  fullsetcestrc  16853  1stfcl  16884  2ndfcl  16885  evlfcl  16909  curf1cl  16915  yonedalem3b  16966  intopsn  17300  mhmpropd  17388  pwssplit1  19107  evls1sca  19736  islindf  20199  rrxds  23227  wlkp1  26634  acunirnmpt  29587  cnmbfm  30453  wrdfd  30744  elmrsubrn  31543  poimirlem3  33542  poimirlem28  33567  isrngod  33827  rngosn3  33853  isgrpda  33884  islfld  34667  tendofset  36363  tendoset  36364  mapfzcons  37596  diophrw  37639  refsum2cnlem1  39510  mgmhmpropd  42110  funcringcsetcALTV2lem9  42369  funcringcsetclem9ALTV  42392  aacllem  42875
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