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Theorem fveq12d 5382
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 5377 . 2 (𝜑 → (𝐹𝐴) = (𝐺𝐴))
3 fveq12d.2 . . 3 (𝜑𝐴 = 𝐵)
43fveq2d 5379 . 2 (𝜑 → (𝐺𝐴) = (𝐺𝐵))
52, 4eqtrd 2147 1 (𝜑 → (𝐹𝐴) = (𝐺𝐵))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1314  cfv 5081
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2244  df-rex 2396  df-v 2659  df-un 3041  df-sn 3499  df-pr 3500  df-op 3502  df-uni 3703  df-br 3896  df-iota 5046  df-fv 5089
This theorem is referenced by:  nffvd  5387  fvsng  5570  tfrlem3ag  6160  tfrlem3a  6161  tfrlemi1  6183  tfr1onlem3ag  6188  omp1eomlem  6931  seq3shft  10503  climshft2  10967  fsum3  11048  ctiunctlemfo  11795  reldvg  12603  dvfvalap  12605
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