Theorem eumoi 2245

Description: "At most one" inferred from existential uniqueness. (Contributed by NM, 5-Apr-1995.)

Hypothesis

Ref	Expression
eumoi.1	|- E!xph

Assertion

Ref	Expression
eumoi	|- E*xph

Proof of Theorem eumoi

Step	Hyp	Ref	Expression
1		eumoi.1	. 2 |- E!xph
2		eumo 2244	. 2 |- (E!xph -> E*xph)
3	1, 2	ax-mp 5	1 |- E*xph

Syntax hints:  E!weu 2204  E*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:  euxfr  3023