Theorem oveqan12rd 5552

Description: Equality deduction for operation value. (Contributed by NM, 10-Aug-1995.)

Hypotheses

Ref	Expression
oveq1d.1	|- ( ph -> A = B )
opreqan12i.2	|- ( ps -> C = D )

Assertion

Ref	Expression
oveqan12rd	|- ( ( ps /\ ph ) -> ( A F C ) = ( B F D ) )

Proof of Theorem oveqan12rd

Step	Hyp	Ref	Expression
1		oveq1d.1	. . 3 |- ( ph -> A = B )
2		opreqan12i.2	. . 3 |- ( ps -> C = D )
3	1, 2	oveqan12d 5551	. 2 |- ( ( ph /\ ps ) -> ( A F C ) = ( B F D ) )
4	3	ancoms 264	1 |- ( ( ps /\ ph ) -> ( A F C ) = ( B F D ) )

Syntax hints:   -> wi 4   /\ wa 102   = wceq 1284  (class class class)co 5532

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 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-3an 921  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-rex 2354  df-v 2603  df-un 2977  df-sn 3404  df-pr 3405  df-op 3407  df-uni 3602  df-br 3786  df-iota 4887  df-fv 4930  df-ov 5535

This theorem is referenced by:  mulresr  7006  recdivap  7806  divgcdcoprm0  10483