Theorem oveq123i 7454

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 7452	. 2 ⊢ (𝐴𝐹𝐵) = (𝐶𝐹𝐷)
4		oveq123i.3	. . 3 ⊢ 𝐹 = 𝐺
5	4	oveqi 7453	. 2 ⊢ (𝐶𝐹𝐷) = (𝐶𝐺𝐷)
6	3, 5	eqtri 2786	1 ⊢ (𝐴𝐹𝐵) = (𝐶𝐺𝐷)

This proof depends on syntax axioms:   = wceq 1570  (class class class)co 7440

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rab 3417  df-v 3456  df-ss 3901  df-dif 4050  df-un 4154  df-nul 4282  df-if 4486  df-sn 4589  df-pr 4591  df-op 4839  df-uni 4871  df-br 5107  df-iota 6509  df-fv 6563  df-ov 7443

This theorem is used by:  relowlpssretop  38478  aks5lem3a  43430  mendvscafval  44378  cytpval  44394  fuconuniqlem  50984  fuconuniqvalslem  50986