Theorem oveqan12rd 5862

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 5861	. 2 |- ( ( ph /\ ps ) -> ( A F C ) = ( B F D ) )
4	3	ancoms 266	1 |- ( ( ps /\ ph ) -> ( A F C ) = ( B F D ) )

Syntax hints:   -> wi 4   /\ wa 103   = wceq 1343  (class class class)co 5842

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 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-3an 970  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-rex 2450  df-v 2728  df-un 3120  df-sn 3582  df-pr 3583  df-op 3585  df-uni 3790  df-br 3983  df-iota 5153  df-fv 5196  df-ov 5845

This theorem is referenced by:  mulresr  7779  recdivap  8614  divgcdcoprm0  12033  dvid  13302