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Theorem fveq1d 5207
Description: Equality deduction for function value. (Contributed by NM, 2-Sep-2003.)
Hypothesis
Ref Expression
fveq1d.1 (𝜑𝐹 = 𝐺)
Assertion
Ref Expression
fveq1d (𝜑 → (𝐹𝐴) = (𝐺𝐴))

Proof of Theorem fveq1d
StepHypRef Expression
1 fveq1d.1 . 2 (𝜑𝐹 = 𝐺)
2 fveq1 5204 . 2 (𝐹 = 𝐺 → (𝐹𝐴) = (𝐺𝐴))
31, 2syl 14 1 (𝜑 → (𝐹𝐴) = (𝐺𝐴))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1259  cfv 4929
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-uni 3608  df-br 3792  df-iota 4894  df-fv 4937
This theorem is referenced by:  fveq12d  5211  funssfv  5226  csbfv2g  5237  fvmptd  5280  fvmpt2d  5284  mpteqb  5288  fvmptt  5289  fmptco  5357  fvunsng  5384  fvsng  5386  fsnunfv  5390  f1ocnvfv1  5444  f1ocnvfv2  5445  fcof1  5450  fcofo  5451  fnofval  5748  offval2  5753  ofrfval2  5754  caofinvl  5760  tfrlemi1  5976  rdg0g  6005  freceq1  6009  oav  6064  omv  6065  oeiv  6066  fseq1p1m1  9057  iseqeq3  9374  iseqid  9405  iseqz  9407  serige0  9411  serile  9412  expival  9416  ibcval5  9624  bcn2  9625  shftcan1  9656  shftcan2  9657  shftvalg  9658  shftval4g  9659  climshft2  10050  iserile  10085
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