Theorem hbeu1 1907

Description: Bound-variable hypothesis builder for uniqueness. (Contributed by NM, 9-Jul-1994.)

Assertion

Ref	Expression
hbeu1	|- (E!xph -> A.xE!xph)

Proof of Theorem hbeu1

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-eu 1900	. 2 |- (E!xph <-> E.yA.x(ph <-> x = y))
2		hba1 1430	. . 3 |- (A.x(ph <-> x = y) -> A.xA.x(ph <-> x = y))
3	2	hbex 1524	. 2 |- (E.yA.x(ph <-> x = y) -> A.xE.yA.x(ph <-> x = y))
4	1, 3	hbxfrbi 1358	1 |- (E!xph -> A.xE!xph)

Syntax hints:   -> wi 4   <-> wb 98  A.wal 1240  E.wex 1378  E!weu 1897

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 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424

This theorem depends on definitions:  df-bi 110  df-eu 1900

This theorem is referenced by:  hbmo1  1935  eupicka  1977  exists2  1994