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Theorem oveq123i 7162
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 7160 . 2 (𝐴𝐹𝐵) = (𝐶𝐹𝐷)
4 oveq123i.3 . . 3 𝐹 = 𝐺
54oveqi 7161 . 2 (𝐶𝐹𝐷) = (𝐶𝐺𝐷)
63, 5eqtri 2842 1 (𝐴𝐹𝐵) = (𝐶𝐺𝐷)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1531  (class class class)co 7148
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1905  ax-6 1964  ax-7 2009  ax-8 2110  ax-9 2118  ax-10 2139  ax-11 2154  ax-12 2170  ax-ext 2791
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1084  df-tru 1534  df-ex 1775  df-nf 1779  df-sb 2064  df-clab 2798  df-cleq 2812  df-clel 2891  df-nfc 2961  df-rex 3142  df-rab 3145  df-v 3495  df-dif 3937  df-un 3939  df-in 3941  df-ss 3950  df-nul 4290  df-if 4466  df-sn 4560  df-pr 4562  df-op 4566  df-uni 4831  df-br 5058  df-iota 6307  df-fv 6356  df-ov 7151
This theorem is referenced by:  relowlpssretop  34637  mendvscafval  39781  cytpval  39800
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