Theorem eumo 2051

Description: Existential uniqueness implies "at most one". (Contributed by NM, 23-Mar-1995.) (Proof rewritten by Jim Kingdon, 27-May-2018.)

Assertion

Ref	Expression
eumo	|- ( E! x ph -> E* x ph )

Proof of Theorem eumo

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 |- ( E! x ph -> ( E. x ph -> E! x ph ) )
2		df-mo 2023	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
3	1, 2	sylibr 133	1 |- ( E! x ph -> E* x ph )

Syntax hints:   -> wi 4   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:  eumoi  2052  eu5  2066  euimmo  2086  moaneu  2095  eupick  2098  2eumo  2107  moeq3dc  2906  nfunsn  5530  fnoprabg  5954  uptx  13068  txcn  13069