Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  oveq123i GIF version

Theorem oveq123i 5526
 Description: Equality inference for operation value. (Contributed by FL, 11-Jul-2010.)
Hypotheses
Ref Expression
oveq123i.1 𝐴 = 𝐶
oveq123i.2 𝐵 = 𝐷
oveq123i.3 𝐹 = 𝐺
Assertion
Ref Expression
oveq123i (𝐴𝐹𝐵) = (𝐶𝐺𝐷)

Proof of Theorem oveq123i
StepHypRef Expression
1 oveq123i.1 . . 3 𝐴 = 𝐶
2 oveq123i.2 . . 3 𝐵 = 𝐷
31, 2oveq12i 5524 . 2 (𝐴𝐹𝐵) = (𝐶𝐹𝐷)
4 oveq123i.3 . . 3 𝐹 = 𝐺
54oveqi 5525 . 2 (𝐶𝐹𝐷) = (𝐶𝐺𝐷)
63, 5eqtri 2060 1 (𝐴𝐹𝐵) = (𝐶𝐺𝐷)
 Colors of variables: wff set class Syntax hints:   = wceq 1243  (class class class)co 5512 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  df-ov 5515 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator