Theorem oveq123i 5796

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 5794	. 2 ⊢ (𝐴𝐹𝐵) = (𝐶𝐹𝐷)
4		oveq123i.3	. . 3 ⊢ 𝐹 = 𝐺
5	4	oveqi 5795	. 2 ⊢ (𝐶𝐹𝐷) = (𝐶𝐺𝐷)
6	3, 5	eqtri 2161	1 ⊢ (𝐴𝐹𝐵) = (𝐶𝐺𝐷)

Syntax hints:   = wceq 1332  (class class class)co 5782

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-v 2691  df-un 3080  df-sn 3538  df-pr 3539  df-op 3541  df-uni 3745  df-br 3938  df-iota 5096  df-fv 5139  df-ov 5785

This theorem is referenced by: (None)