Theorem hbmo1 2092

Description: Bound-variable hypothesis builder for "at most one". (Contributed by NM, 8-Mar-1995.)

Assertion

Ref	Expression
hbmo1	|- ( E* x ph -> A. x E* x ph )

Proof of Theorem hbmo1

Step	Hyp	Ref	Expression
1		df-mo 2058	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
2		hbe1 1518	. . 3 |- ( E. x ph -> A. x E. x ph )
3		hbeu1 2064	. . 3 |- ( E! x ph -> A. x E! x ph )
4	2, 3	hbim 1568	. 2 |- ( ( E. x ph -> E! x ph ) -> A. x ( E. x ph -> E! x ph ) )
5	1, 4	hbxfrbi 1495	1 |- ( E* x ph -> A. x E* x ph )

Syntax hints:   -> wi 4   A.wal 1371   E.wex 1515   E!weu 2054   E*wmo 2055

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-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-ial 1557  ax-i5r 1558

This theorem depends on definitions:  df-bi 117  df-eu 2057  df-mo 2058

This theorem is referenced by:  mopick2  2137  moexexdc  2138