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Theorem moan 2363
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 467 . 2  |-  ( ( ps  /\  ph )  ->  ph )
21moimi 2359 1  |-  ( E* x ph  ->  E* x ( ps  /\  ph ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 375   E*wmo 2310
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-10 1925  ax-12 1943
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1674  df-nf 1678  df-eu 2313  df-mo 2314
This theorem is referenced by:  moani  2364  mooran1  2366  moanim  2368  mormo  3018  rmoan  3249
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