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Theorem mooran1 2337
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
StepHypRef Expression
1 simpl 445 . . 3  |-  ( (
ph  /\  ps )  ->  ph )
21moimi 2330 . 2  |-  ( E* x ph  ->  E* x ( ph  /\  ps ) )
3 moan 2334 . 2  |-  ( E* x ps  ->  E* x ( ph  /\  ps ) )
42, 3jaoi 370 1  |-  ( ( E* x ph  \/  E* x ps )  ->  E* x ( ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 359    /\ wa 360   E*wmo 2284
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288
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