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Theorem mooran1 2197
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 443 . . 3  |-  ( (
ph  /\  ps )  ->  ph )
21moimi 2190 . 2  |-  ( E* x ph  ->  E* x ( ph  /\  ps ) )
3 moan 2194 . 2  |-  ( E* x ps  ->  E* x ( ph  /\  ps ) )
42, 3jaoi 368 1  |-  ( ( E* x ph  \/  E* x ps )  ->  E* x ( ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 357    /\ wa 358   E*wmo 2144
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148
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