Theorem moan 2066

Description: "At most one" is still the case when a conjunct is added. (Contributed by NM, 22-Apr-1995.)

Assertion

Ref	Expression
moan	|- ( E* x ph -> E* x ( ps /\ ph ) )

Proof of Theorem moan

Step	Hyp	Ref	Expression
1		simpr 109	. 2 |- ( ( ps /\ ph ) -> ph )
2	1	moimi 2062	1 |- ( E* x ph -> E* x ( ps /\ ph ) )

Syntax hints:   -> wi 4   /\ wa 103   E*wmo 1998

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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-eu 2000  df-mo 2001

This theorem is referenced by:  moani  2067  mooran1  2069  mormo  2640  rmoan  2879