Theorem hbimd 1815

Description: Deduction form of bound-variable hypothesis builder hbim 1817. (Contributed by NM, 1-Jan-2002.) (Proof shortened by Wolf Lammen, 3-Jan-2018.)

Hypotheses

Ref	Expression
hbimd.1	|- (ph -> A.xph)
hbimd.2	|- (ph -> (ps -> A.xps))
hbimd.3	|- (ph -> (ch -> A.xch))

Assertion

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

Proof of Theorem hbimd

Step	Hyp	Ref	Expression
1		hbimd.1	. . . 4 |- (ph -> A.xph)
2		hbimd.2	. . . 4 |- (ph -> (ps -> A.xps))
3	1, 2	nfdh 1767	. . 3 |- (ph -> F/xps)
4		hbimd.3	. . . 4 |- (ph -> (ch -> A.xch))
5	1, 4	nfdh 1767	. . 3 |- (ph -> F/xch)
6	3, 5	nfimd 1808	. 2 |- (ph -> F/x(ps -> ch))
7	6	nfrd 1763	1 |- (ph -> ((ps -> ch) -> A.x(ps -> ch)))

Syntax hints:   -> wi 4  A.wal 1540

This theorem was proved from 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 theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545

This theorem is referenced by:  spimehOLD  1821  dvelimhw  1849  dvelimv  1939  dvelimh  1964  dvelimALT  2133  dvelimf-o  2180