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Theorem feq1d 5116
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 5112 . 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 103   = wceq 1287  wf 4979
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2617  df-un 2992  df-in 2994  df-ss 3001  df-sn 3437  df-pr 3438  df-op 3440  df-br 3823  df-opab 3877  df-rel 4420  df-cnv 4421  df-co 4422  df-dm 4423  df-rn 4424  df-fun 4985  df-fn 4986  df-f 4987
This theorem is referenced by:  feq12d  5118  fco2  5143  fssres2  5153  fresin  5154  fmpt3d  5419  fmptco  5429  fressnfv  5449  off  5827  caofinvl  5836  f2ndf  5950  eroprf  6339  pmresg  6387  fseq1p1m1  9441
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