Theorem oveq123i 5864

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	|- ( A F B ) = ( C G D )

Proof of Theorem oveq123i

Step	Hyp	Ref	Expression
1		oveq123i.1	. . 3 |- A = C
2		oveq123i.2	. . 3 |- B = D
3	1, 2	oveq12i 5862	. 2 |- ( A F B ) = ( C F D )
4		oveq123i.3	. . 3 |- F = G
5	4	oveqi 5863	. 2 |- ( C F D ) = ( C G D )
6	3, 5	eqtri 2191	1 |- ( A F B ) = ( C G D )

Syntax hints:   = wceq 1348  (class class class)co 5850

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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-3an 975  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-rex 2454  df-v 2732  df-un 3125  df-sn 3587  df-pr 3588  df-op 3590  df-uni 3795  df-br 3988  df-iota 5158  df-fv 5204  df-ov 5853

This theorem is referenced by: (None)