Theorem hbnt 710

Description: A closed form of hypothesis builder hbne 699.

Assertion

Ref	Expression
hbnt	|- (A.x(ph -> A.xph) -> (-. ph -> A.x -. ph))

Proof of Theorem hbnt

Step	Hyp	Ref	Expression
1		con3 86	. . 3 |- ((ph -> A.xph) -> (-. A.xph -> -. ph))
2	1	19.20ii 692	. 2 |- (A.x(ph -> A.xph) -> (A.x -. A.xph -> A.x -. ph))
3		ax-6 675	. . 3 |- (-. A.x -. A.xph -> ph)
4	3	con1i 88	. 2 |- (-. ph -> A.x -. A.xph)
5	2, 4	syl5 22	1 |- (A.x(ph -> A.xph) -> (-. ph -> A.x -. ph))

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

This theorem is referenced by:  19.9t 719  hbnd 786

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

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