Theorem mooran2 2118

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 2116	. 2 |- ( E* x ( ph \/ ps ) -> E* x ph )
2		olc 712	. . 3 |- ( ps -> ( ph \/ ps ) )
3	2	moimi 2110	. 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 2046

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-sb 1777  df-eu 2048  df-mo 2049

This theorem is referenced by: (None)