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Theorem moaneu 2018
Description: Nested "at most one" and uniqueness quantifiers. (Contributed by NM, 25-Jan-2006.)
Assertion
Ref Expression
moaneu  |-  E* x
( ph  /\  E! x ph )

Proof of Theorem moaneu
StepHypRef Expression
1 eumo 1974 . . 3  |-  ( E! x ph  ->  E* x ph )
2 nfeu1 1953 . . . 4  |-  F/ x E! x ph
32moanim 2016 . . 3  |-  ( E* x ( E! x ph  /\  ph )  <->  ( E! x ph  ->  E* x ph ) )
41, 3mpbir 144 . 2  |-  E* x
( E! x ph  /\ 
ph )
5 ancom 262 . . 3  |-  ( (
ph  /\  E! x ph )  <->  ( E! x ph  /\  ph ) )
65mobii 1979 . 2  |-  ( E* x ( ph  /\  E! x ph )  <->  E* x
( E! x ph  /\ 
ph ) )
74, 6mpbir 144 1  |-  E* x
( ph  /\  E! x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102   E!weu 1942   E*wmo 1943
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946
This theorem is referenced by: (None)
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