Theorem mooran2 2129

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 2127	. 2 |- ( E* x ( ph \/ ps ) -> E* x ph )
2		olc 713	. . 3 |- ( ps -> ( ph \/ ps ) )
3	2	moimi 2121	. 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 710   E*wmo 2056

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-eu 2058  df-mo 2059

This theorem is referenced by: (None)