Theorem mooran2 2070

Description: "At most one" exports disjunction to conjunction. (Contributed by NM, 5-Apr-2004.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)

Assertion

Ref	Expression
mooran2	|- ( E* x ( ph \/ ps ) -> ( E* x ph /\ E* x ps ) )

Proof of Theorem mooran2

Step	Hyp	Ref	Expression
1		moor 2068	. 2 |- ( E* x ( ph \/ ps ) -> E* x ph )
2		olc 700	. . 3 |- ( ps -> ( ph \/ ps ) )
3	2	moimi 2062	. 2 |- ( E* x ( ph \/ ps ) -> E* x ps )
4	1, 3	jca 304	1 |- ( E* x ( ph \/ ps ) -> ( E* x ph /\ E* x ps ) )

Syntax hints:   -> wi 4   /\ wa 103   \/ wo 697   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: (None)