Theorem moabs 1949

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		pm5.4 238	. 2 |- ( ( E. x ph -> ( E. x ph -> E! x ph ) ) <-> ( E. x ph -> E! x ph ) )
2		df-mo 1904	. . 3 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
3	2	imbi2i 215	. 2 |- ( ( E. x ph -> E* x ph ) <-> ( E. x ph -> ( E. x ph -> E! x ph ) ) )
4	1, 3, 2	3bitr4ri 202	1 |- ( E* x ph <-> ( E. x ph -> E* x ph ) )

Syntax hints:   -> wi 4   <-> wb 98   E.wex 1381   E!weu 1900   E*wmo 1901

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-mo 1904

This theorem is referenced by:  mo2icl  2720  dffun7  4928