Theorem 19.9t 1076

Description: A closed version of one direction of 19.9 1077.

Assertion

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

Proof of Theorem 19.9t

Step	Hyp	Ref	Expression
1		hbnt 1043	. . 3 |- (A.x(ph -> A.xph) -> (-. ph -> A.x -. ph))
2	1	con1d 97	. 2 |- (A.x(ph -> A.xph) -> (-. A.x -. ph -> ph))
3		df-ex 1022	. 2 |- (E.xph <-> -. A.x -. ph)
4	2, 3	syl5ib 213	1 |- (A.x(ph -> A.xph) -> (E.xph -> ph))

Syntax hints:  -. wn 2   -> wi 3  A.wal 995  E.wex 1021

This theorem is referenced by:  19.9 1077  19.9d 1078  exists2 1503

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1004  ax-4 1014  ax-5o 1016  ax-6o 1019

This theorem depends on definitions:  df-bi 154  df-ex 1022

Copyright terms: Public domain