Theorem 19.21hOLD 1840

Description: Obsolete proof of 19.21h 1797 as of 1-Jan-2018. (Contributed by NM, 1-Aug-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
19.21hOLD.1	|- (ph -> A.xph)

Assertion

Ref	Expression
19.21hOLD	|- (A.x(ph -> ps) <-> (ph -> A.xps))

Proof of Theorem 19.21hOLD

Step	Hyp	Ref	Expression
1		19.21hOLD.1	. . 3 |- (ph -> A.xph)
2		alim 1558	. . 3 |- (A.x(ph -> ps) -> (A.xph -> A.xps))
3	1, 2	syl5 28	. 2 |- (A.x(ph -> ps) -> (ph -> A.xps))
4		hba1 1786	. . . 4 |- (A.xps -> A.xA.xps)
5	1, 4	hbim 1817	. . 3 |- ((ph -> A.xps) -> A.x(ph -> A.xps))
6		sp 1747	. . . 4 |- (A.xps -> ps)
7	6	imim2i 13	. . 3 |- ((ph -> A.xps) -> (ph -> ps))
8	5, 7	alrimih 1565	. 2 |- ((ph -> A.xps) -> A.x(ph -> ps))
9	3, 8	impbii 180	1 |- (A.x(ph -> ps) <-> (ph -> A.xps))

Syntax hints:   -> wi 4   <-> wb 176  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: (None)