Theorem eumo 2244

Description: Existential uniqueness implies "at most one." (Contributed by NM, 23-Mar-1995.)

Assertion

Ref	Expression
eumo	⊢ (∃!xφ → ∃*xφ)

Proof of Theorem eumo

Step	Hyp	Ref	Expression
1		eu5 2242	. 2 ⊢ (∃!xφ ↔ (∃xφ ∧ ∃*xφ))
2	1	simprbi 450	1 ⊢ (∃!xφ → ∃*xφ)

Syntax hints:   → wi 4  ∃wex 1541  ∃!weu 2204  ∃*wmo 2205

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209

This theorem is referenced by:  eumoi  2245  euimmo  2253  moaneu  2263  eupick  2267  2eumo  2277  2exeu  2281  2eu2  2285  2eu5  2288  moeq3  3014  nfunsn  5354  dff3  5421  fnoprabg  5586