Theorem oveq123i 5526

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 5524	. 2 |- ( A F B ) = ( C F D )
4		oveq123i.3	. . 3 |- F = G
5	4	oveqi 5525	. 2 |- ( C F D ) = ( C G D )
6	3, 5	eqtri 2060	1 |- ( A F B ) = ( C G D )

Syntax hints:   = wceq 1243  (class class class)co 5512

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910  df-ov 5515

This theorem is referenced by: (None)