Theorem mooran1 2527

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 473	. . 3 |- ( ( ph /\ ps ) -> ph )
2	1	moimi 2520	. 2 |- ( E* x ph -> E* x ( ph /\ ps ) )
3		moan 2524	. 2 |- ( E* x ps -> E* x ( ph /\ ps ) )
4	2, 3	jaoi 394	1 |- ( ( E* x ph \/ E* x ps ) -> E* x ( ph /\ ps ) )

Syntax hints:   -> wi 4   \/ wo 383   /\ wa 384   E*wmo 2471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-eu 2474  df-mo 2475

This theorem is referenced by: (None)