Theorem hbnt 1894

Description: Closed theorem version of bound-variable hypothesis builder hbn 1895. (Contributed by NM, 10-May-1993.) (Proof shortened by Wolf Lammen, 3-Mar-2018.)

Assertion

Ref	Expression
hbnt

Proof of Theorem hbnt

Step	Hyp	Ref	Expression
1		df-ex 1613	. . 3
2		19.9ht 1889	. . 3
3	1, 2	syl5bir 218	. 2
4	3	con1d 124	1

Syntax hints:  -.wn 3  ->wi 4  A.wal 1393  E.wex 1612

This theorem is referenced by:  hbn  1895  nfnt  1900  hbnd  1974  bj-hbext  34264

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854

This theorem depends on definitions:  df-bi 185  df-ex 1613