Theorem oveq123i 6092

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 6090	. 2 |- ( A F B ) = ( C F D )
4		oveq123i.3	. . 3 |- F = G
5	4	oveqi 6091	. 2 |- ( C F D ) = ( C G D )
6	3, 5	eqtri 2259	1 |- ( A F B ) = ( C G D )

Syntax hints:   = wceq 1402  (class class class)co 6078

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-3an 1011  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-rex 2534  df-v 2823  df-un 3224  df-sn 3714  df-pr 3715  df-op 3717  df-uni 3934  df-br 4129  df-iota 5335  df-fv 5383  df-ov 6081

This theorem is referenced by: (None)