Theorem exmoeu2 2128

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 2127	. 2 |- ( E! x ph <-> ( E. x ph /\ E* x ph ) )
2	1	baibr 927	1 |- ( E. x ph -> ( E* x ph <-> E! x ph ) )

Syntax hints:   -> wi 4   <-> wb 105   E.wex 1540   E!weu 2079   E*wmo 2080

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811  df-eu 2082  df-mo 2083

This theorem is referenced by:  n0mmoeu  3511  fneu  5436