Theorem oveq123i 5781

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 5779	. 2 |- ( A F B ) = ( C F D )
4		oveq123i.3	. . 3 |- F = G
5	4	oveqi 5780	. 2 |- ( C F D ) = ( C G D )
6	3, 5	eqtri 2158	1 |- ( A F B ) = ( C G D )

Syntax hints:   = wceq 1331  (class class class)co 5767

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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420  df-v 2683  df-un 3070  df-sn 3528  df-pr 3529  df-op 3531  df-uni 3732  df-br 3925  df-iota 5083  df-fv 5126  df-ov 5770

This theorem is referenced by: (None)