Theorem eumo 2031

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 2003	. 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 1468   E!weu 1999   E*wmo 2000

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 2003

This theorem is referenced by:  eumoi  2032  eu5  2046  euimmo  2066  moaneu  2075  eupick  2078  2eumo  2087  moeq3dc  2860  nfunsn  5455  fnoprabg  5872  uptx  12443  txcn  12444