Theorem hbeu1 1421

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 1035	. . 3 |- (A.x(ph <-> x = y) -> A.xA.x(ph <-> x = y))
2	1	hbex 1038	. 2 |- (E.yA.x(ph <-> x = y) -> A.xE.yA.x(ph <-> x = y))
3		df-eu 1415	. 2 |- (E!xph <-> E.yA.x(ph <-> x = y))
4	3	albii 1031	. 2 |- (A.xE!xph <-> A.xE.yA.x(ph <-> x = y))
5	2, 3, 4	3imtr4i 217	1 |- (E!xph -> A.xE!xph)

Syntax hints:   -> wi 3   <-> wb 144  A.wal 986  E.wex 1012  E!weu 1413

This theorem is referenced by:  hbmo1 1439  moaneu 1463  eupicka 1468  2eu8 1490  hbreu1 1806  dffun8 3615  fneu 3667  fv3 3809  tz6.12c 3816  aceq5lem5 4825

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 994  ax-gen 995  ax-4 1005  ax-5o 1007  ax-6o 1010

This theorem depends on definitions:  df-bi 145  df-an 223  df-ex 1013  df-eu 1415

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