Theorem 19.9t 1031

Description: A closed version of one direction of 19.9 1032.

Assertion

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

Proof of Theorem 19.9t

Step	Hyp	Ref	Expression
1		hbnt 999	. . 3 |- (A.x(ph -> A.xph) -> (-. ph -> A.x -. ph))
2	1	con1d 93	. 2 |- (A.x(ph -> A.xph) -> (-. A.x -. ph -> ph))
3		df-ex 978	. 2 |- (E.xph <-> -. A.x -. ph)
4	2, 3	syl5ib 206	1 |- (A.x(ph -> A.xph) -> (E.xph -> ph))

Syntax hints:  -. wn 2   -> wi 3  A.wal 951  E.wex 977

This theorem is referenced by:  19.9 1032  19.9d 1033  exists2 1451

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 960  ax-4 970  ax-5o 972  ax-6o 975

This theorem depends on definitions:  df-bi 147  df-ex 978

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