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Theorem fveq12i 6153
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 6149 . 2 (𝐹𝐴) = (𝐺𝐴)
3 fveq12i.2 . . 3 𝐴 = 𝐵
43fveq2i 6151 . 2 (𝐺𝐴) = (𝐺𝐵)
52, 4eqtri 2643 1 (𝐹𝐴) = (𝐺𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  cfv 5847
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-rex 2913  df-rab 2916  df-v 3188  df-dif 3558  df-un 3560  df-in 3562  df-ss 3569  df-nul 3892  df-if 4059  df-sn 4149  df-pr 4151  df-op 4155  df-uni 4403  df-br 4614  df-iota 5810  df-fv 5855
This theorem is referenced by:  cats1fvn  13540  sadcadd  15104  sadadd2  15106  coe1fzgsumdlem  19590  evl1gsumdlem  19639  madufval  20362  2wlkond  26702  1pthond  26870  3cycld  26904  kur14lem5  30897  fourierdlem62  39689  fouriersw  39752
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