Theorem hbeu1 1394

Description: Bound-variable hypothesis builder for uniqueness.

Assertion

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

Proof of Theorem hbeu1

Step	Hyp	Ref	Expression
1		hba1 1009	. . 3 |- (A.x(ph <-> x = y) -> A.xA.x(ph <-> x = y))
2	1	hbex 1012	. 2 |- (E.yA.x(ph <-> x = y) -> A.xE.yA.x(ph <-> x = y))
3		df-eu 1388	. 2 |- (E!xph <-> E.yA.x(ph <-> x = y))
4	3	albii 1005	. 2 |- (A.xE!xph <-> A.xE.yA.x(ph <-> x = y))
5	2, 3, 4	3imtr4 219	1 |- (E!xph -> A.xE!xph)

Syntax hints:   -> wi 3   <-> wb 146  A.wal 958  E.wex 984  E!weu 1386

This theorem is referenced by:  hbmo1 1412  moaneu 1436  eupicka 1441  2eu8 1463  hbreu1 1775  dffun7 3554  fneu 3606  fv3 3747  tz6.12c 3754  aceq5lem5 4751

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 966  ax-gen 967  ax-4 977  ax-5o 979  ax-6o 982

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 985  df-eu 1388

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