Theorem hbmo1 2035

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 2001	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
2		hbe1 1471	. . 3 |- ( E. x ph -> A. x E. x ph )
3		hbeu1 2007	. . 3 |- ( E! x ph -> A. x E! x ph )
4	2, 3	hbim 1524	. 2 |- ( ( E. x ph -> E! x ph ) -> A. x ( E. x ph -> E! x ph ) )
5	1, 4	hbxfrbi 1448	1 |- ( E* x ph -> A. x E* x ph )

Syntax hints:   -> wi 4   A.wal 1329   E.wex 1468   E!weu 1997   E*wmo 1998

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514  ax-i5r 1515

This theorem depends on definitions:  df-bi 116  df-eu 2000  df-mo 2001

This theorem is referenced by:  mopick2  2080  moexexdc  2081