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Theorem moan 2207
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 447 . 2  |-  ( ( ps  /\  ph )  ->  ph )
21moimi 2203 1  |-  ( E* x ph  ->  E* x ( ps  /\  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   E*wmo 2157
This theorem is referenced by:  moani  2208  mooran1  2210  mormo  2765  rmoan  2976
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161
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