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Theorem oveq123i 7372
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 7370 . 2 (𝐴𝐹𝐵) = (𝐶𝐹𝐷)
4 oveq123i.3 . . 3 𝐹 = 𝐺
54oveqi 7371 . 2 (𝐶𝐹𝐷) = (𝐶𝐺𝐷)
63, 5eqtri 2765 1 (𝐴𝐹𝐵) = (𝐶𝐺𝐷)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  (class class class)co 7358
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-rab 3409  df-v 3448  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-if 4488  df-sn 4588  df-pr 4590  df-op 4594  df-uni 4867  df-br 5107  df-iota 6449  df-fv 6505  df-ov 7361
This theorem is referenced by:  relowlpssretop  35838  mendvscafval  41520  cytpval  41539
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