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Theorem mooran1 2085
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 108 . . 3  |-  ( (
ph  /\  ps )  ->  ph )
21moimi 2078 . 2  |-  ( E* x ph  ->  E* x ( ph  /\  ps ) )
3 moan 2082 . 2  |-  ( E* x ps  ->  E* x ( ph  /\  ps ) )
42, 3jaoi 706 1  |-  ( ( E* x ph  \/  E* x ps )  ->  E* x ( ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    \/ wo 698   E*wmo 2014
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522
This theorem depends on definitions:  df-bi 116  df-nf 1448  df-sb 1750  df-eu 2016  df-mo 2017
This theorem is referenced by: (None)
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