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Theorem fveq12d 5534
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 5529 . 2 (𝜑 → (𝐹𝐴) = (𝐺𝐴))
3 fveq12d.2 . . 3 (𝜑𝐴 = 𝐵)
43fveq2d 5531 . 2 (𝜑 → (𝐺𝐴) = (𝐺𝐵))
52, 4eqtrd 2220 1 (𝜑 → (𝐹𝐴) = (𝐺𝐵))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1363  cfv 5228
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 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-3an 981  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-rex 2471  df-v 2751  df-un 3145  df-sn 3610  df-pr 3611  df-op 3613  df-uni 3822  df-br 4016  df-iota 5190  df-fv 5236
This theorem is referenced by:  nffvd  5539  fvsng  5725  tfrlem3ag  6323  tfrlem3a  6324  tfrlemi1  6346  tfr1onlem3ag  6351  omp1eomlem  7106  seq3shft  10860  climshft2  11327  fsum3  11408  ctiunctlemfo  12453  imasival  12744  mulgfvalg  13013  mulgval  13014  mulgnndir  13041  mulgpropdg  13054  unitinvinv  13355  rlmvalg  13606  rsp0  13644  reldvg  14375  dvfvalap  14377  lgsval  14632  lgsneg  14652
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