Theorem exmonim 1951

Description: There is at most one of something which does not exist. Unlike exmodc 1950 there is no decidability condition. (Contributed by Jim Kingdon, 22-Sep-2018.)

Assertion

Ref	Expression
exmonim	|- ( -. E. x ph -> E* x ph )

Proof of Theorem exmonim

Step	Hyp	Ref	Expression
1		pm2.21 547	. 2 |- ( -. E. x ph -> ( E. x ph -> E! x ph ) )
2		df-mo 1904	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
3	1, 2	sylibr 137	1 |- ( -. E. x ph -> E* x ph )

Syntax hints:   -. wn 3   -> wi 4   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  ax-in2 545

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

This theorem is referenced by: (None)