Theorem mooran1 2015

Description: "At most one" imports disjunction to conjunction. (Contributed by NM, 5-Apr-2004.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)

Assertion

Ref	Expression
mooran1	|- ( ( E* x ph \/ E* x ps ) -> E* x ( ph /\ ps ) )

Proof of Theorem mooran1

Step	Hyp	Ref	Expression
1		simpl 107	. . 3 |- ( ( ph /\ ps ) -> ph )
2	1	moimi 2008	. 2 |- ( E* x ph -> E* x ( ph /\ ps ) )
3		moan 2012	. 2 |- ( E* x ps -> E* x ( ph /\ ps ) )
4	2, 3	jaoi 669	1 |- ( ( E* x ph \/ E* x ps ) -> E* x ( ph /\ ps ) )

Syntax hints:   -> wi 4   /\ wa 102   \/ wo 662   E*wmo 1944

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469

This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-eu 1946  df-mo 1947

This theorem is referenced by: (None)