Theorem mooran2 2367

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 2365	. 2 |- ( E* x ( ph \/ ps ) -> E* x ph )
2		olc 390	. . 3 |- ( ps -> ( ph \/ ps ) )
3	2	moimi 2359	. 2 |- ( E* x ( ph \/ ps ) -> E* x ps )
4	1, 3	jca 539	1 |- ( E* x ( ph \/ ps ) -> ( E* x ph /\ E* x ps ) )

Syntax hints:   -> wi 4   \/ wo 374   /\ wa 375   E*wmo 2310

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-10 1925  ax-12 1943

This theorem depends on definitions:  df-bi 190  df-or 376  df-an 377  df-ex 1674  df-nf 1678  df-eu 2313  df-mo 2314

This theorem is referenced by: (None)