Theorem hbnd 1467

Description: Deduction form of bound-variable hypothesis builder hbn 1351.

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 1345	. 2 |- (ph -> A.x(ps -> A.xps))
4		hbnt 1349	. 2 |- (A.x(ps -> A.xps) -> (-. ps -> A.x -. ps))
5	3, 4	syl 12	1 |- (ph -> (-. ps -> A.x -. ps))

Syntax hints:  -. wn 2   -> wi 3  A.wal 1296

This theorem is referenced by:  hbimd 1468  cbvexd 1704  a12studyALT 1770  copsexg 3537  axpowndlem2 6102  axpowndlem3 6103  axpowndlem4 6104  axregndlem2 6107  axregnd 6108  distel 13870

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-4 1319  ax-5o 1321  ax-6o 1324

Copyright terms: Public domain