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Theorem fveq12d 5437
 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 5432 . 2 (𝜑 → (𝐹𝐴) = (𝐺𝐴))
3 fveq12d.2 . . 3 (𝜑𝐴 = 𝐵)
43fveq2d 5434 . 2 (𝜑 → (𝐺𝐴) = (𝐺𝐵))
52, 4eqtrd 2173 1 (𝜑 → (𝐹𝐴) = (𝐺𝐵))
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1332  ‘cfv 5132 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-v 2692  df-un 3081  df-sn 3539  df-pr 3540  df-op 3542  df-uni 3746  df-br 3939  df-iota 5097  df-fv 5140 This theorem is referenced by:  nffvd  5442  fvsng  5625  tfrlem3ag  6215  tfrlem3a  6216  tfrlemi1  6238  tfr1onlem3ag  6243  omp1eomlem  6989  seq3shft  10662  climshft2  11127  fsum3  11208  ctiunctlemfo  12008  reldvg  12876  dvfvalap  12878
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