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Theorem fveq12d 5503
Description: Equality deduction for function value. (Contributed by FL, 22-Dec-2008.)
Hypotheses
Ref Expression
fveq12d.1  |-  ( ph  ->  F  =  G )
fveq12d.2  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
fveq12d  |-  ( ph  ->  ( F `  A
)  =  ( G `
 B ) )

Proof of Theorem fveq12d
StepHypRef Expression
1 fveq12d.1 . . 3  |-  ( ph  ->  F  =  G )
21fveq1d 5498 . 2  |-  ( ph  ->  ( F `  A
)  =  ( G `
 A ) )
3 fveq12d.2 . . 3  |-  ( ph  ->  A  =  B )
43fveq2d 5500 . 2  |-  ( ph  ->  ( G `  A
)  =  ( G `
 B ) )
52, 4eqtrd 2203 1  |-  ( ph  ->  ( F `  A
)  =  ( G `
 B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1348   ` cfv 5198
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-rex 2454  df-v 2732  df-un 3125  df-sn 3589  df-pr 3590  df-op 3592  df-uni 3797  df-br 3990  df-iota 5160  df-fv 5206
This theorem is referenced by:  nffvd  5508  fvsng  5692  tfrlem3ag  6288  tfrlem3a  6289  tfrlemi1  6311  tfr1onlem3ag  6316  omp1eomlem  7071  seq3shft  10802  climshft2  11269  fsum3  11350  ctiunctlemfo  12394  reldvg  13442  dvfvalap  13444  lgsval  13699  lgsneg  13719
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