Theorem hbnd 1111

Description: Deduction form of bound-variable hypothesis builder hbn 1006.

Hypotheses

Ref	Expression
hbnd.1	|- (ph -> A.xph)
hbnd.2	|- (ph -> (ps -> A.xps))

Assertion

Ref	Expression
hbnd	|- (ph -> (-. ps -> A.x -. ps))

Proof of Theorem hbnd

Step	Hyp	Ref	Expression
1		hbnd.1	. . 3 |- (ph -> A.xph)
2		hbnd.2	. . 3 |- (ph -> (ps -> A.xps))
3	1, 2	19.21ai 1000	. 2 |- (ph -> A.x(ps -> A.xps))
4		hbnt 1004	. 2 |- (A.x(ps -> A.xps) -> (-. ps -> A.x -. ps))
5	3, 4	syl 10	1 |- (ph -> (-. ps -> A.x -. ps))

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

This theorem is referenced by:  hbimd 1112  cbvexd 1323  a12studyALT 1381  axpowndlem2 4962  axpowndlem3 4963  axpowndlem4 4964  axregndlem2 4967  axregnd 4968

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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