Theorem hbnt 1004

Description: Closed theorem version of bound-variable hypothesis builder hbn 1006.

Assertion

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

Proof of Theorem hbnt

Step	Hyp	Ref	Expression
1		con3 94	. . 3 |- ((ph -> A.xph) -> (-. A.xph -> -. ph))
2	1	19.20ii 997	. 2 |- (A.x(ph -> A.xph) -> (A.x -. A.xph -> A.x -. ph))
3		ax-6o 980	. . 3 |- (-. A.x -. A.xph -> ph)
4	3	con1i 96	. 2 |- (-. ph -> A.x -. A.xph)
5	2, 4	syl5 21	1 |- (A.x(ph -> A.xph) -> (-. ph -> A.x -. ph))

Syntax hints:  -. wn 2   -> wi 3  A.wal 956

This theorem is referenced by:  hbn 1006  19.9t 1037  hbnd 1111

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-4 975  ax-5o 977  ax-6o 980

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