Theorem oveqan12rd 5987

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 5986	. 2 |- ( ( ph /\ ps ) -> ( A F C ) = ( B F D ) )
4	3	ancoms 268	1 |- ( ( ps /\ ph ) -> ( A F C ) = ( B F D ) )

Syntax hints:   -> wi 4   /\ wa 104   = wceq 1373  (class class class)co 5967

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-rex 2492  df-v 2778  df-un 3178  df-sn 3649  df-pr 3650  df-op 3652  df-uni 3865  df-br 4060  df-iota 5251  df-fv 5298  df-ov 5970

This theorem is referenced by:  mulresr  7986  recdivap  8826  divgcdcoprm0  12538  ismhm  13408  dvid  15282  dvidre  15284