Theorem 19.23hOLD 1820

Description: Obsolete proof of 19.23h 1802 as of 1-Jan-2018. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
19.23hOLD.1	|- (ps -> A.xps)

Assertion

Ref	Expression
19.23hOLD	|- (A.x(ph -> ps) <-> (E.xph -> ps))

Proof of Theorem 19.23hOLD

Step	Hyp	Ref	Expression
1		exim 1575	. . 3 |- (A.x(ph -> ps) -> (E.xph -> E.xps))
2		19.23hOLD.1	. . . 4 |- (ps -> A.xps)
3	2	19.9h 1780	. . 3 |- (E.xps <-> ps)
4	1, 3	syl6ib 217	. 2 |- (A.x(ph -> ps) -> (E.xph -> ps))
5		hbe1 1731	. . . 4 |- (E.xph -> A.xE.xph)
6	5, 2	hbim 1817	. . 3 |- ((E.xph -> ps) -> A.x(E.xph -> ps))
7		19.8a 1756	. . . 4 |- (ph -> E.xph)
8	7	imim1i 54	. . 3 |- ((E.xph -> ps) -> (ph -> ps))
9	6, 8	alrimih 1565	. 2 |- ((E.xph -> ps) -> A.x(ph -> ps))
10	4, 9	impbii 180	1 |- (A.x(ph -> ps) <-> (E.xph -> ps))

Syntax hints:   -> wi 4   <-> wb 176  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)