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Theorem feq1d 5229
Description: Equality deduction for functions. (Contributed by NM, 19-Feb-2008.)
Hypothesis
Ref Expression
feq1d.1 (𝜑𝐹 = 𝐺)
Assertion
Ref Expression
feq1d (𝜑 → (𝐹:𝐴𝐵𝐺:𝐴𝐵))

Proof of Theorem feq1d
StepHypRef Expression
1 feq1d.1 . 2 (𝜑𝐹 = 𝐺)
2 feq1 5225 . 2 (𝐹 = 𝐺 → (𝐹:𝐴𝐵𝐺:𝐴𝐵))
31, 2syl 14 1 (𝜑 → (𝐹:𝐴𝐵𝐺:𝐴𝐵))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104   = wceq 1316  wf 5089
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-sn 3503  df-pr 3504  df-op 3506  df-br 3900  df-opab 3960  df-rel 4516  df-cnv 4517  df-co 4518  df-dm 4519  df-rn 4520  df-fun 5095  df-fn 5096  df-f 5097
This theorem is referenced by:  feq12d  5232  fco2  5259  fssres2  5270  fresin  5271  fmpt3d  5544  fmptco  5554  fressnfv  5575  off  5962  caofinvl  5972  f2ndf  6091  eroprf  6490  pmresg  6538  fseq1p1m1  9842  lmbr  12309  blfps  12505  blf  12506  dvmptclx  12776
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