Theorem hbnd 1883

Description: Deduction form of bound-variable hypothesis builder hbn 1776. (Contributed by NM, 3-Jan-2002.)

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	alrimih 1565	. 2 |- (ph -> A.x(ps -> A.xps))
4		hbnt 1775	. 2 |- (A.x(ps -> A.xps) -> (-. ps -> A.x -. ps))
5	3, 4	syl 15	1 |- (ph -> (-. ps -> A.x -. ps))

This proof depends on syntax axioms:  -. wn 3   -> wi 4  A.wal 1540

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This proof depends on definitions:  df-bi 177  df-ex 1542

This theorem is used by: (None)