Theorem exmoeu2 2093

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 2092	. 2 |- ( E! x ph <-> ( E. x ph /\ E* x ph ) )
2	1	baibr 921	1 |- ( E. x ph -> ( E* x ph <-> E! x ph ) )

Syntax hints:   -> wi 4   <-> wb 105   E.wex 1506   E!weu 2045   E*wmo 2046

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 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-sb 1777  df-eu 2048  df-mo 2049

This theorem is referenced by:  n0mmoeu  3467  fneu  5362