Theorem hbmo1 1979

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 1945	. 2 |- ( E* x ph <-> ( E. x ph -> E! x ph ) )
2		hbe1 1424	. . 3 |- ( E. x ph -> A. x E. x ph )
3		hbeu1 1951	. . 3 |- ( E! x ph -> A. x E! x ph )
4	2, 3	hbim 1477	. 2 |- ( ( E. x ph -> E! x ph ) -> A. x ( E. x ph -> E! x ph ) )
5	1, 4	hbxfrbi 1401	1 |- ( E* x ph -> A. x E* x ph )

Syntax hints:   -> wi 4   A.wal 1282   E.wex 1421   E!weu 1941   E*wmo 1942

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-ial 1467  ax-i5r 1468

This theorem depends on definitions:  df-bi 115  df-eu 1944  df-mo 1945

This theorem is referenced by:  mopick2  2024  moexexdc  2025