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Theorem fveq12i 5696
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  |-  ( F `
 A )  =  ( G `  B
)

Proof of Theorem fveq12i
StepHypRef Expression
1 fveq12i.1 . . 3  |-  F  =  G
21fveq1i 5692 . 2  |-  ( F `
 A )  =  ( G `  A
)
3 fveq12i.2 . . 3  |-  A  =  B
43fveq2i 5694 . 2  |-  ( G `
 A )  =  ( G `  B
)
52, 4eqtri 2463 1  |-  ( F `
 A )  =  ( G `  B
)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1369   ` cfv 5418
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-rex 2721  df-rab 2724  df-v 2974  df-dif 3331  df-un 3333  df-in 3335  df-ss 3342  df-nul 3638  df-if 3792  df-sn 3878  df-pr 3880  df-op 3884  df-uni 4092  df-br 4293  df-iota 5381  df-fv 5426
This theorem is referenced by:  cats1fvn  12485  sadcadd  13654  sadadd2  13656  evl1gsumdlem  17790  madufval  18443  kur14lem5  27098  coe1fzgsumdlem  30837
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