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Theorem fveq12d 5537
Description: Equality deduction for function value. (Contributed by FL, 22-Dec-2008.)
Hypotheses
Ref Expression
fveq12d.1 (𝜑𝐹 = 𝐺)
fveq12d.2 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
fveq12d (𝜑 → (𝐹𝐴) = (𝐺𝐵))

Proof of Theorem fveq12d
StepHypRef Expression
1 fveq12d.1 . . 3 (𝜑𝐹 = 𝐺)
21fveq1d 5532 . 2 (𝜑 → (𝐹𝐴) = (𝐺𝐴))
3 fveq12d.2 . . 3 (𝜑𝐴 = 𝐵)
43fveq2d 5534 . 2 (𝜑 → (𝐺𝐴) = (𝐺𝐵))
52, 4eqtrd 2222 1 (𝜑 → (𝐹𝐴) = (𝐺𝐵))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1364  cfv 5231
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-rex 2474  df-v 2754  df-un 3148  df-sn 3613  df-pr 3614  df-op 3616  df-uni 3825  df-br 4019  df-iota 5193  df-fv 5239
This theorem is referenced by:  nffvd  5542  fvsng  5728  tfrlem3ag  6328  tfrlem3a  6329  tfrlemi1  6351  tfr1onlem3ag  6356  omp1eomlem  7111  seq3shft  10865  climshft2  11332  fsum3  11413  ctiunctlemfo  12458  imasival  12749  mulgfvalg  13029  mulgval  13030  mulgnndir  13057  mulgpropdg  13070  unitinvinv  13435  rlmvalg  13731  rsp0  13770  znval  13893  reldvg  14545  dvfvalap  14547  lgsval  14802  lgsneg  14822
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