Theorem moan 2095

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 110	. 2 |- ( ( ps /\ ph ) -> ph )
2	1	moimi 2091	1 |- ( E* x ph -> E* x ( ps /\ ph ) )

Syntax hints:   -> wi 4   /\ wa 104   E*wmo 2027

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030

This theorem is referenced by:  moani  2096  mooran1  2098  mormo  2688  rmoan  2937