Theorem exlimdh 1807

Description: Deduction from Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 28-Jan-1997.)

Hypotheses

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

Assertion

Ref	Expression
exlimdh	|- (ph -> (E.xps -> ch))

Proof of Theorem exlimdh

Step	Hyp	Ref	Expression
1		exlimdh.1	. . 3 |- (ph -> A.xph)
2	1	nfi 1551	. 2 |- F/xph
3		exlimdh.2	. . 3 |- (ch -> A.xch)
4	3	nfi 1551	. 2 |- F/xch
5		exlimdh.3	. 2 |- (ph -> (ps -> ch))
6	2, 4, 5	exlimd 1806	1 |- (ph -> (E.xps -> ch))

Syntax hints:   -> wi 4  A.wal 1540  E.wex 1541

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: (None)