Theorem hbmo1 2064

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 2030	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
2		hbe1 1495	. . 3 |- ( E. x ph -> A. x E. x ph )
3		hbeu1 2036	. . 3 |- ( E! x ph -> A. x E! x ph )
4	2, 3	hbim 1545	. 2 |- ( ( E. x ph -> E! x ph ) -> A. x ( E. x ph -> E! x ph ) )
5	1, 4	hbxfrbi 1472	1 |- ( E* x ph -> A. x E* x ph )

Syntax hints:   -> wi 4   A.wal 1351   E.wex 1492   E!weu 2026   E*wmo 2027

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534  ax-i5r 1535

This theorem depends on definitions:  df-bi 117  df-eu 2029  df-mo 2030

This theorem is referenced by:  mopick2  2109  moexexdc  2110