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Theorem fveq12i 6658
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 6653 . 2 (𝐹𝐴) = (𝐺𝐴)
3 fveq12i.2 . . 3 𝐴 = 𝐵
43fveq2i 6655 . 2 (𝐺𝐴) = (𝐺𝐵)
52, 4eqtri 2845 1 (𝐹𝐴) = (𝐺𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  cfv 6334
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-ext 2794
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-ex 1782  df-sb 2070  df-clab 2801  df-cleq 2815  df-clel 2894  df-v 3471  df-un 3913  df-in 3915  df-ss 3925  df-sn 4540  df-pr 4542  df-op 4546  df-uni 4814  df-br 5043  df-iota 6293  df-fv 6342
This theorem is referenced by:  cats1fvn  14211  sadcadd  15796  sadadd2  15798  coe1fzgsumdlem  20928  evl1gsumdlem  20978  madufval  21240  clwlkcompbp  27569  2wlkond  27721  1pthond  27927  3cycld  27961  2cycld  32459  kur14lem5  32531  bj-ndxarg  34453  fourierdlem62  42749  fouriersw  42812  ackval41a  45047  ackval42  45049
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