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Theorem fveq12d 5396
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 5391 . 2 (𝜑 → (𝐹𝐴) = (𝐺𝐴))
3 fveq12d.2 . . 3 (𝜑𝐴 = 𝐵)
43fveq2d 5393 . 2 (𝜑 → (𝐺𝐴) = (𝐺𝐵))
52, 4eqtrd 2150 1 (𝜑 → (𝐹𝐴) = (𝐺𝐵))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1316  cfv 5093
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-rex 2399  df-v 2662  df-un 3045  df-sn 3503  df-pr 3504  df-op 3506  df-uni 3707  df-br 3900  df-iota 5058  df-fv 5101
This theorem is referenced by:  nffvd  5401  fvsng  5584  tfrlem3ag  6174  tfrlem3a  6175  tfrlemi1  6197  tfr1onlem3ag  6202  omp1eomlem  6947  seq3shft  10578  climshft2  11043  fsum3  11124  ctiunctlemfo  11879  reldvg  12744  dvfvalap  12746
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