Theorem mooran2 2153

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 2151	. 2 |- ( E* x ( ph \/ ps ) -> E* x ph )
2		olc 718	. . 3 |- ( ps -> ( ph \/ ps ) )
3	2	moimi 2145	. 2 |- ( E* x ( ph \/ ps ) -> E* x ps )
4	1, 3	jca 306	1 |- ( E* x ( ph \/ ps ) -> ( E* x ph /\ E* x ps ) )

Syntax hints:   -> wi 4   /\ wa 104   \/ wo 715   E*wmo 2080

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811  df-eu 2082  df-mo 2083

This theorem is referenced by: (None)