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Theorem oveq123i 6810
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 6808 . 2 (𝐴𝐹𝐵) = (𝐶𝐹𝐷)
4 oveq123i.3 . . 3 𝐹 = 𝐺
54oveqi 6809 . 2 (𝐶𝐹𝐷) = (𝐶𝐺𝐷)
63, 5eqtri 2793 1 (𝐴𝐹𝐵) = (𝐶𝐺𝐷)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1631  (class class class)co 6796
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-3an 1073  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-rex 3067  df-rab 3070  df-v 3353  df-dif 3726  df-un 3728  df-in 3730  df-ss 3737  df-nul 4064  df-if 4227  df-sn 4318  df-pr 4320  df-op 4324  df-uni 4576  df-br 4788  df-iota 5993  df-fv 6038  df-ov 6799
This theorem is referenced by:  relowlpssretop  33549  mendvscafval  38286  cytpval  38313
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