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Theorem fveq12i 6108
 Description: Equality deduction for function value. (Contributed by FL, 27-Jun-2014.)
Hypotheses
Ref Expression
fveq12i.1 𝐹 = 𝐺
fveq12i.2 𝐴 = 𝐵
Assertion
Ref Expression
fveq12i (𝐹𝐴) = (𝐺𝐵)

Proof of Theorem fveq12i
StepHypRef Expression
1 fveq12i.1 . . 3 𝐹 = 𝐺
21fveq1i 6104 . 2 (𝐹𝐴) = (𝐺𝐴)
3 fveq12i.2 . . 3 𝐴 = 𝐵
43fveq2i 6106 . 2 (𝐺𝐴) = (𝐺𝐵)
52, 4eqtri 2632 1 (𝐹𝐴) = (𝐺𝐵)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475  ‘cfv 5804 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rex 2902  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-uni 4373  df-br 4584  df-iota 5768  df-fv 5812 This theorem is referenced by:  cats1fvn  13454  sadcadd  15018  sadadd2  15020  coe1fzgsumdlem  19492  evl1gsumdlem  19541  madufval  20262  kur14lem5  30446  fourierdlem62  39061  fouriersw  39124  21wlkond  41144  1pthond  41311  3cycld  41345
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