Theorem 19.21tOLD 1863

Description: Obsolete proof of 19.21t 1795 as of 30-Dec-2017. (Contributed by NM, 27-May-1997.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
19.21tOLD	|- ( F/xph -> (A.x(ph -> ps) <-> (ph -> A.xps)))

Proof of Theorem 19.21tOLD

Step	Hyp	Ref	Expression
1		id 19	. . . 4 |- ( F/xph -> F/xph)
2	1	nfrd 1763	. . 3 |- ( F/xph -> (ph -> A.xph))
3		alim 1558	. . 3 |- (A.x(ph -> ps) -> (A.xph -> A.xps))
4	2, 3	syl9 66	. 2 |- ( F/xph -> (A.x(ph -> ps) -> (ph -> A.xps)))
5		nfa1 1788	. . . . . 6 |- F/xA.xps
6	5	a1i 10	. . . . 5 |- ( F/xph -> F/xA.xps)
7	1, 6	nfimd 1808	. . . 4 |- ( F/xph -> F/x(ph -> A.xps))
8	7	nfrd 1763	. . 3 |- ( F/xph -> ((ph -> A.xps) -> A.x(ph -> A.xps)))
9		sp 1747	. . . . 5 |- (A.xps -> ps)
10	9	imim2i 13	. . . 4 |- ((ph -> A.xps) -> (ph -> ps))
11	10	alimi 1559	. . 3 |- (A.x(ph -> A.xps) -> A.x(ph -> ps))
12	8, 11	syl6 29	. 2 |- ( F/xph -> ((ph -> A.xps) -> A.x(ph -> ps)))
13	4, 12	impbid 183	1 |- ( F/xph -> (A.x(ph -> ps) <-> (ph -> A.xps)))

Syntax hints:   -> wi 4   <-> wb 176  A.wal 1540   F/wnf 1544

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)