Theorem exmoeu2 2008

Description: Existence implies "at most one" is equivalent to uniqueness. (Contributed by NM, 5-Apr-2004.)

Assertion

Ref	Expression
exmoeu2	|- ( E. x ph -> ( E* x ph <-> E! x ph ) )

Proof of Theorem exmoeu2

Step	Hyp	Ref	Expression
1		eu5 2007	. 2 |- ( E! x ph <-> ( E. x ph /\ E* x ph ) )
2	1	baibr 873	1 |- ( E. x ph -> ( E* x ph <-> E! x ph ) )

Syntax hints:   -> wi 4   <-> wb 104   E.wex 1436   E!weu 1960   E*wmo 1961

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483

This theorem depends on definitions:  df-bi 116  df-nf 1405  df-sb 1704  df-eu 1963  df-mo 1964

This theorem is referenced by:  n0mmoeu  3326  fneu  5163