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Theorem moanmo 1977
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 19 . . 3  |-  ( E* x ph  ->  E* x ph )
2 nfmo1 1912 . . . 4  |-  F/ x E* x ph
32moanim 1974 . . 3  |-  ( E* x ( E* x ph  /\  ph )  <->  ( E* x ph  ->  E* x ph ) )
41, 3mpbir 134 . 2  |-  E* x
( E* x ph  /\ 
ph )
5 ancom 253 . . 3  |-  ( (
ph  /\  E* x ph )  <->  ( E* x ph  /\  ph ) )
65mobii 1937 . 2  |-  ( E* x ( ph  /\  E* x ph )  <->  E* x
( E* x ph  /\ 
ph ) )
74, 6mpbir 134 1  |-  E* x
( ph  /\  E* x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 97   E*wmo 1901
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904
This theorem is referenced by: (None)
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