Theorem mooran2 2115

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 2113	. 2 |- ( E* x ( ph \/ ps ) -> E* x ph )
2		olc 712	. . 3 |- ( ps -> ( ph \/ ps ) )
3	2	moimi 2107	. 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 709   E*wmo 2043

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-eu 2045  df-mo 2046

This theorem is referenced by: (None)