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Theorem mooran2 2367
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
StepHypRef Expression
1 moor 2365 . 2  |-  ( E* x ( ph  \/  ps )  ->  E* x ph )
2 olc 390 . . 3  |-  ( ps 
->  ( ph  \/  ps ) )
32moimi 2359 . 2  |-  ( E* x ( ph  \/  ps )  ->  E* x ps )
41, 3jca 539 1  |-  ( E* x ( ph  \/  ps )  ->  ( E* x ph  /\  E* x ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    \/ wo 374    /\ wa 375   E*wmo 2310
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-10 1925  ax-12 1943
This theorem depends on definitions:  df-bi 190  df-or 376  df-an 377  df-ex 1674  df-nf 1678  df-eu 2313  df-mo 2314
This theorem is referenced by: (None)
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