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Theorem oveq123i 7440
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 7438 . 2 (𝐴𝐹𝐵) = (𝐶𝐹𝐷)
4 oveq123i.3 . . 3 𝐹 = 𝐺
54oveqi 7439 . 2 (𝐶𝐹𝐷) = (𝐶𝐺𝐷)
63, 5eqtri 2756 1 (𝐴𝐹𝐵) = (𝐶𝐺𝐷)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  (class class class)co 7426
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2706  df-cleq 2720  df-clel 2806  df-rab 3431  df-v 3475  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4327  df-if 4533  df-sn 4633  df-pr 4635  df-op 4639  df-uni 4913  df-br 5153  df-iota 6505  df-fv 6561  df-ov 7429
This theorem is referenced by:  relowlpssretop  36876  mendvscafval  42645  cytpval  42661
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