Theorem mon 2053

Description: There is at most one of something which does not exist. (Contributed by Jim Kingdon, 5-Jul-2018.)

Assertion

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

Proof of Theorem mon

Step	Hyp	Ref	Expression
1		ax-in2 615	. 2 |- ( -. E. x ph -> ( E. x ph -> E! x ph ) )
2		df-mo 2028	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
3	1, 2	sylibr 134	1 |- ( -. E. x ph -> E* x ph )

Syntax hints:   -. wn 3   -> wi 4   E.wex 1490   E!weu 2024   E*wmo 2025

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in2 615

This theorem depends on definitions:  df-bi 117  df-mo 2028

This theorem is referenced by:  moexexdc  2108