Theorem hbmo1 2057

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 2023	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
2		hbe1 1488	. . 3 |- ( E. x ph -> A. x E. x ph )
3		hbeu1 2029	. . 3 |- ( E! x ph -> A. x E! x ph )
4	2, 3	hbim 1538	. 2 |- ( ( E. x ph -> E! x ph ) -> A. x ( E. x ph -> E! x ph ) )
5	1, 4	hbxfrbi 1465	1 |- ( E* x ph -> A. x E* x ph )

Syntax hints:   -> wi 4   A.wal 1346   E.wex 1485   E!weu 2019   E*wmo 2020

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 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-ial 1527  ax-i5r 1528

This theorem depends on definitions:  df-bi 116  df-eu 2022  df-mo 2023

This theorem is referenced by:  mopick2  2102  moexexdc  2103