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Theorem fveq12i 5871
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 5867 . 2  |-  ( F `
 A )  =  ( G `  A
)
3 fveq12i.2 . . 3  |-  A  =  B
43fveq2i 5869 . 2  |-  ( G `
 A )  =  ( G `  B
)
52, 4eqtri 2496 1  |-  ( F `
 A )  =  ( G `  B
)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1379   ` cfv 5588
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rex 2820  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-uni 4246  df-br 4448  df-iota 5551  df-fv 5596
This theorem is referenced by:  cats1fvn  12789  sadcadd  13970  sadadd2  13972  coe1fzgsumdlem  18154  evl1gsumdlem  18203  madufval  18946  kur14lem5  28405  fourierdlem62  31696  fouriersw  31759
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