Theorem oveq123i 7434

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 7432	. 2 ⊢ (𝐴𝐹𝐵) = (𝐶𝐹𝐷)
4		oveq123i.3	. . 3 ⊢ 𝐹 = 𝐺
5	4	oveqi 7433	. 2 ⊢ (𝐶𝐹𝐷) = (𝐶𝐺𝐷)
6	3, 5	eqtri 2783	1 ⊢ (𝐴𝐹𝐵) = (𝐶𝐺𝐷)

This proof depends on syntax axioms:   = wceq 1569  (class class class)co 7420

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-rab 3413  df-v 3452  df-ss 3896  df-dif 4047  df-un 4151  df-nul 4279  df-if 4482  df-sn 4584  df-pr 4586  df-op 4590  df-uni 4867  df-br 5103  df-iota 6494  df-fv 6546  df-ov 7423

This theorem is used by:  relowlpssretop  38288  aks5lem3a  43240  mendvscafval  44188  cytpval  44204