Theorem hbeu1 1365

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 979	. . 3 |- (A.x(ph <-> x = y) -> A.xA.x(ph <-> x = y))
2	1	hbex 982	. 2 |- (E.yA.x(ph <-> x = y) -> A.xE.yA.x(ph <-> x = y))
3		df-eu 1359	. 2 |- (E!xph <-> E.yA.x(ph <-> x = y))
4	3	albii 975	. 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 950  E.wex 956  E!weu 1357

This theorem is referenced by:  hbmo1 1383  moaneu 1407  2eu8 1433  hbreu1 1744  dffun7 3481  fneu 3532  fv3 3672  tz6.12c 3679  aceq5lem5 4663

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 951  ax-5 952  ax-6 953  ax-7 954  ax-gen 955

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 957  df-eu 1359

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