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Theorem fveq12i 5517
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 5512 . 2  |-  ( F `
 A )  =  ( G `  A
)
3 fveq12i.2 . . 3  |-  A  =  B
43fveq2i 5514 . 2  |-  ( G `
 A )  =  ( G `  B
)
52, 4eqtri 2198 1  |-  ( F `
 A )  =  ( G `  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1353   ` cfv 5212
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rex 2461  df-v 2739  df-un 3133  df-sn 3597  df-pr 3598  df-op 3600  df-uni 3808  df-br 4001  df-iota 5174  df-fv 5220
This theorem is referenced by: (None)
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