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Theorem moan 2331
Description: "At most one" is still the case when a conjunct is added. (Contributed by NM, 22-Apr-1995.)
Assertion
Ref Expression
moan  |-  ( E* x ph  ->  E* x ( ps  /\  ph ) )

Proof of Theorem moan
StepHypRef Expression
1 simpr 448 . 2  |-  ( ( ps  /\  ph )  ->  ph )
21moimi 2327 1  |-  ( E* x ph  ->  E* x ( ps  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359   E*wmo 2281
This theorem is referenced by:  moani  2332  mooran1  2334  mormo  2912  rmoan  3124
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285
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