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Theorem fveq12i 5210
 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 5206 . 2 (𝐹𝐴) = (𝐺𝐴)
3 fveq12i.2 . . 3 𝐴 = 𝐵
43fveq2i 5208 . 2 (𝐺𝐴) = (𝐺𝐵)
52, 4eqtri 2076 1 (𝐹𝐴) = (𝐺𝐵)
 Colors of variables: wff set class Syntax hints:   = wceq 1259  ‘cfv 4929 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-v 2576  df-un 2949  df-sn 3408  df-pr 3409  df-op 3411  df-uni 3608  df-br 3792  df-iota 4894  df-fv 4937 This theorem is referenced by: (None)
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