Theorem hbmo1 2083

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 2049	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
2		hbe1 1509	. . 3 |- ( E. x ph -> A. x E. x ph )
3		hbeu1 2055	. . 3 |- ( E! x ph -> A. x E! x ph )
4	2, 3	hbim 1559	. 2 |- ( ( E. x ph -> E! x ph ) -> A. x ( E. x ph -> E! x ph ) )
5	1, 4	hbxfrbi 1486	1 |- ( E* x ph -> A. x E* x ph )

Syntax hints:   -> wi 4   A.wal 1362   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-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-ial 1548  ax-i5r 1549

This theorem depends on definitions:  df-bi 117  df-eu 2048  df-mo 2049

This theorem is referenced by:  mopick2  2128  moexexdc  2129