Theorem exmoeu2 1948

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 1947	. 2 |- ( E! x ph <-> ( E. x ph /\ E* x ph ) )
2	1	baibr 829	1 |- ( E. x ph -> ( E* x ph <-> E! x ph ) )

Syntax hints:   -> wi 4   <-> wb 98   E.wex 1381   E!weu 1900   E*wmo 1901

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904

This theorem is referenced by:  n0mmoeu  3237  fneu  5003