Theorem 19.9ht 1778

Description: A closed version of 19.9 1783. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
19.9ht	|- (A.x(ph -> A.xph) -> (E.xph -> ph))

Proof of Theorem 19.9ht

Step	Hyp	Ref	Expression
1		df-ex 1542	. 2 |- (E.xph <-> -. A.x -. ph)
2		hbnt 1775	. . 3 |- (A.x(ph -> A.xph) -> (-. ph -> A.x -. ph))
3	2	con1d 116	. 2 |- (A.x(ph -> A.xph) -> (-. A.x -. ph -> ph))
4	1, 3	syl5bi 208	1 |- (A.x(ph -> A.xph) -> (E.xph -> ph))

Syntax hints:  -. wn 3   -> wi 4  A.wal 1540  E.wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by:  19.9t  1779  19.9hOLD  1781