Theorem eumo 2058

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 2030	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
3	1, 2	sylibr 134	1 |- ( E! x ph -> E* x ph )

Syntax hints:   -> wi 4   E.wex 1492   E!weu 2026   E*wmo 2027

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

This theorem depends on definitions:  df-bi 117  df-mo 2030

This theorem is referenced by:  eumoi  2059  eu5  2073  euimmo  2093  moaneu  2102  eupick  2105  2eumo  2114  moeq3dc  2915  nfunsn  5551  fnoprabg  5978  uptx  13859  txcn  13860