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Theorem moabs 1991
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 pm5.4 247 . 2  |-  ( ( E. x ph  ->  ( E. x ph  ->  E! x ph ) )  <-> 
( E. x ph  ->  E! x ph )
)
2 df-mo 1946 . . 3  |-  ( E* x ph  <->  ( E. x ph  ->  E! x ph ) )
32imbi2i 224 . 2  |-  ( ( E. x ph  ->  E* x ph )  <->  ( E. x ph  ->  ( E. x ph  ->  E! x ph ) ) )
41, 3, 23bitr4ri 211 1  |-  ( E* x ph  <->  ( E. x ph  ->  E* x ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   E.wex 1422   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
This theorem depends on definitions:  df-bi 115  df-mo 1946
This theorem is referenced by:  mo2icl  2772  dffun7  4958
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