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Theorem fveq12i 5183
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 (𝐹𝐴) = (𝐺𝐵)

Proof of Theorem fveq12i
StepHypRef Expression
1 fveq12i.1 . . 3 𝐹 = 𝐺
21fveq1i 5179 . 2 (𝐹𝐴) = (𝐺𝐴)
3 fveq12i.2 . . 3 𝐴 = 𝐵
43fveq2i 5181 . 2 (𝐺𝐴) = (𝐺𝐵)
52, 4eqtri 2060 1 (𝐹𝐴) = (𝐺𝐵)
Colors of variables: wff set class
Syntax hints:   = wceq 1243  cfv 4902
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910
This theorem is referenced by: (None)
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