Theorem 19.9t 719

Description: A closed version of one direction of 19.9r 718.

Assertion

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

Proof of Theorem 19.9t

Step	Hyp	Ref	Expression
1		hbnt 710	. . 3 |- (A.x(ph -> A.xph) -> (-. ph -> A.x -. ph))
2	1	con1d 85	. 2 |- (A.x(ph -> A.xph) -> (-. A.x -. ph -> ph))
3		df-ex 679	. 2 |- (E.xph <-> -. A.x -. ph)
4	2, 3	syl5ib 181	1 |- (A.x(ph -> A.xph) -> (E.xph -> ph))

Syntax hints:  -. wn 1   -> wi 2  A.wal 672  E.wex 678

This theorem is referenced by:  19.9d 720  exists2 1073

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-ex 679

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