Theorem 19.9t 1035

Description: A closed version of one direction of 19.9 1036.

Assertion

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

Proof of Theorem 19.9t

Step	Hyp	Ref	Expression
1		hbnt 1002	. . 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 981	. 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 954  E.wex 980

This theorem is referenced by:  19.9 1036  19.9d 1037  exists2 1458

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975  ax-6o 978

This theorem depends on definitions:  df-bi 147  df-ex 981

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