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Theorem mooran2 2021
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 2019 . 2  |-  ( E* x ( ph  \/  ps )  ->  E* x ph )
2 olc 667 . . 3  |-  ( ps 
->  ( ph  \/  ps ) )
32moimi 2013 . 2  |-  ( E* x ( ph  \/  ps )  ->  E* x ps )
41, 3jca 300 1  |-  ( E* x ( ph  \/  ps )  ->  ( E* x ph  /\  E* x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    \/ wo 664   E*wmo 1949
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952
This theorem is referenced by: (None)
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