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Theorem moabs 2068
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 pm5.4 248 . 2  |-  ( ( E. x ph  ->  ( E. x ph  ->  E! x ph ) )  <-> 
( E. x ph  ->  E! x ph )
)
2 df-mo 2023 . . 3  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
32imbi2i 225 . 2  |-  ( ( E. x ph  ->  E* x ph )  <->  ( E. x ph  ->  ( E. x ph  ->  E! x ph ) ) )
41, 3, 23bitr4ri 212 1  |-  ( E* x ph  <->  ( E. x ph  ->  E* x ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   E.wex 1485   E!weu 2019   E*wmo 2020
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-mo 2023
This theorem is referenced by:  mo2icl  2909  dffun7  5223
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