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Theorem moabs 2200
Description: Absorption of existence condition by "at most one." (Contributed by NM, 4-Nov-2002.)
Assertion
Ref Expression
moabs  |-  ( E* x ph  <->  ( E. x ph  ->  E* x ph ) )

Proof of Theorem moabs
StepHypRef Expression
1 pm5.4 351 . 2  |-  ( ( E. x ph  ->  ( E. x ph  ->  E! x ph ) )  <-> 
( E. x ph  ->  E! x ph )
)
2 df-mo 2161 . . 3  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
32imbi2i 303 . 2  |-  ( ( E. x ph  ->  E* x ph )  <->  ( E. x ph  ->  ( E. x ph  ->  E! x ph ) ) )
41, 3, 23bitr4ri 269 1  |-  ( E* x ph  <->  ( E. x ph  ->  E* x ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   E.wex 1531   E!weu 2156   E*wmo 2157
This theorem is referenced by:  dffun7  5296
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-mo 2161
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