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Theorem fveq12i 5395
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 5390 . 2  |-  ( F `
 A )  =  ( G `  A
)
3 fveq12i.2 . . 3  |-  A  =  B
43fveq2i 5392 . 2  |-  ( G `
 A )  =  ( G `  B
)
52, 4eqtri 2138 1  |-  ( F `
 A )  =  ( G `  B
)
Colors of variables: wff set class
Syntax hints:    = wceq 1316   ` cfv 5093
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-rex 2399  df-v 2662  df-un 3045  df-sn 3503  df-pr 3504  df-op 3506  df-uni 3707  df-br 3900  df-iota 5058  df-fv 5101
This theorem is referenced by: (None)
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