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Theorem fveq12i 5126
 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 5122 . 2 (𝐹A) = (𝐺A)
3 fveq12i.2 . . 3 A = B
43fveq2i 5124 . 2 (𝐺A) = (𝐺B)
52, 4eqtri 2057 1 (𝐹A) = (𝐺B)
 Colors of variables: wff set class Syntax hints:   = wceq 1242  ‘cfv 4845 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853 This theorem is referenced by: (None)
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