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Theorem moanmo 2371
Description: Nested "at most one" quantifiers. (Contributed by NM, 25-Jan-2006.)
Assertion
Ref Expression
moanmo  |-  E* x
( ph  /\  E* x ph )

Proof of Theorem moanmo
StepHypRef Expression
1 id 22 . . 3  |-  ( E* x ph  ->  E* x ph )
2 nfmo1 2320 . . . 4  |-  F/ x E* x ph
32moanim 2368 . . 3  |-  ( E* x ( E* x ph  /\  ph )  <->  ( E* x ph  ->  E* x ph ) )
41, 3mpbir 214 . 2  |-  E* x
( E* x ph  /\ 
ph )
5 ancom 456 . . 3  |-  ( (
ph  /\  E* x ph )  <->  ( E* x ph  /\  ph ) )
65mobii 2332 . 2  |-  ( E* x ( ph  /\  E* x ph )  <->  E* x
( E* x ph  /\ 
ph ) )
74, 6mpbir 214 1  |-  E* x
( ph  /\  E* x 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-11 1930  ax-12 1943
This theorem depends on definitions:  df-bi 190  df-or 376  df-an 377  df-tru 1457  df-ex 1674  df-nf 1678  df-eu 2313  df-mo 2314
This theorem is referenced by:  moaneu  2372
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