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

Step	Hyp	Ref	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 ) )
3	2	imbi2i 225	. 2 |- ( ( E. x ph -> E* x ph ) <-> ( E. x ph -> ( E. x ph -> E! x ph ) ) )
4	1, 3, 2	3bitr4ri 212	1 |- ( E* x ph <-> ( E. x ph -> E* x ph ) )

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  5225