Theorem oveq123i 5627

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 5625	. 2 |- ( A F B ) = ( C F D )
4		oveq123i.3	. . 3 |- F = G
5	4	oveqi 5626	. 2 |- ( C F D ) = ( C G D )
6	3, 5	eqtri 2105	1 |- ( A F B ) = ( C G D )

Syntax hints:   = wceq 1287  (class class class)co 5613

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067

This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rex 2361  df-v 2617  df-un 2992  df-sn 3437  df-pr 3438  df-op 3440  df-uni 3637  df-br 3821  df-iota 4946  df-fv 4989  df-ov 5616

This theorem is referenced by: (None)