Theorem moabs 2501

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		pm5.4 377	. 2 |- ( ( E. x ph -> ( E. x ph -> E! x ph ) ) <-> ( E. x ph -> E! x ph ) )
2		df-mo 2475	. . 3 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
3	2	imbi2i 326	. 2 |- ( ( E. x ph -> E* x ph ) <-> ( E. x ph -> ( E. x ph -> E! x ph ) ) )
4	1, 3, 2	3bitr4ri 293	1 |- ( E* x ph <-> ( E. x ph -> E* x ph ) )

Syntax hints:   -> wi 4   <-> wb 196   E.wex 1704   E!weu 2470   E*wmo 2471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-mo 2475

This theorem is referenced by:  mo3  2507  dffun7  5915  bj-mo3OLD  32832  wl-mo3t  33358