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Theorem feq23d 6274
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 2827 . 2 (𝜑𝐹 = 𝐹)
2 feq23d.1 . 2 (𝜑𝐴 = 𝐶)
3 feq23d.2 . 2 (𝜑𝐵 = 𝐷)
41, 2, 3feq123d 6268 1 (𝜑 → (𝐹:𝐴𝐵𝐹:𝐶𝐷))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 198   = wceq 1658  wf 6120
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-13 2391  ax-ext 2804
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-3an 1115  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-clab 2813  df-cleq 2819  df-clel 2822  df-nfc 2959  df-rab 3127  df-v 3417  df-dif 3802  df-un 3804  df-in 3806  df-ss 3813  df-nul 4146  df-if 4308  df-sn 4399  df-pr 4401  df-op 4405  df-br 4875  df-opab 4937  df-rel 5350  df-cnv 5351  df-co 5352  df-dm 5353  df-rn 5354  df-fun 6126  df-fn 6127  df-f 6128
This theorem is referenced by:  nvof1o  6792  axdc4uz  13079  isacs  16665  isfunc  16877  funcres  16909  funcpropd  16913  estrcco  17123  funcestrcsetclem9  17142  fullestrcsetc  17145  fullsetcestrc  17160  1stfcl  17191  2ndfcl  17192  evlfcl  17216  curf1cl  17222  yonedalem3b  17273  intopsn  17607  mhmpropd  17695  pwssplit1  19419  evls1sca  20049  islindf  20519  rrxds  23562  wlkp1  26983  acunirnmpt  30009  cnmbfm  30871  wrdfd  31163  elmrsubrn  31964  poimirlem3  33957  poimirlem28  33982  isrngod  34240  rngosn3  34266  isgrpda  34297  islfld  35138  tendofset  36834  tendoset  36835  mapfzcons  38124  diophrw  38167  refsum2cnlem1  40015  mgmhmpropd  42633  funcringcsetcALTV2lem9  42892  funcringcsetclem9ALTV  42915  aacllem  43444
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