Theorem oveqan12rd 5942

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 5941	. 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 1364  (class class class)co 5922

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 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-rex 2481  df-v 2765  df-un 3161  df-sn 3628  df-pr 3629  df-op 3631  df-uni 3840  df-br 4034  df-iota 5219  df-fv 5266  df-ov 5925

This theorem is referenced by:  mulresr  7905  recdivap  8745  divgcdcoprm0  12269  ismhm  13093  dvid  14931  dvidre  14933