Theorem hbmo1 1938

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 1904	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
2		hbe1 1384	. . 3 |- ( E. x ph -> A. x E. x ph )
3		hbeu1 1910	. . 3 |- ( E! x ph -> A. x E! x ph )
4	2, 3	hbim 1437	. 2 |- ( ( E. x ph -> E! x ph ) -> A. x ( E. x ph -> E! x ph ) )
5	1, 4	hbxfrbi 1361	1 |- ( E* x ph -> A. x E* x ph )

Syntax hints:   -> wi 4   A.wal 1241   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-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427  ax-i5r 1428

This theorem depends on definitions:  df-bi 110  df-eu 1903  df-mo 1904

This theorem is referenced by:  mopick2  1983  moexexdc  1984