Theorem oveq123i 7404

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

Step	Hyp	Ref	Expression
1		oveq123i.1	. . 3 ⊢ 𝐴 = 𝐶
2		oveq123i.2	. . 3 ⊢ 𝐵 = 𝐷
3	1, 2	oveq12i 7402	. 2 ⊢ (𝐴𝐹𝐵) = (𝐶𝐹𝐷)
4		oveq123i.3	. . 3 ⊢ 𝐹 = 𝐺
5	4	oveqi 7403	. 2 ⊢ (𝐶𝐹𝐷) = (𝐶𝐺𝐷)
6	3, 5	eqtri 2753	1 ⊢ (𝐴𝐹𝐵) = (𝐶𝐺𝐷)

Syntax hints:   = wceq 1540  (class class class)co 7390

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-rab 3409  df-v 3452  df-dif 3920  df-un 3922  df-ss 3934  df-nul 4300  df-if 4492  df-sn 4593  df-pr 4595  df-op 4599  df-uni 4875  df-br 5111  df-iota 6467  df-fv 6522  df-ov 7393

This theorem is referenced by:  relowlpssretop  37359  aks5lem3a  42184  mendvscafval  43182  cytpval  43198