Theorem eujustALT 2285

Description: Alternate proof of eujust 2284 illustrating the use of dvelim 2079. (Contributed by NM, 11-Mar-2010.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
eujustALT

Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem eujustALT

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		equequ2 1799	. . . . . 6
2	1	bibi2d 318	. . . . 5
3	2	albidv 1713	. . . 4
4	3	sps 1865	. . 3
5	4	drex1 2069	. 2
6		hbnae 2057	. . . . . 6
7		hbnae 2057	. . . . . 6
8	6, 7	alrimih 1642	. . . . 5
9		ax-5 1704	. . . . . . . 8
10		equequ2 1799	. . . . . . . . . . 11
11	10	bibi2d 318	. . . . . . . . . 10
12	11	albidv 1713	. . . . . . . . 9
13	12	notbid 294	. . . . . . . 8
14	9, 13	dvelim 2079	. . . . . . 7
15	14	naecoms 2053	. . . . . 6
16		ax-5 1704	. . . . . . 7
17		equequ2 1799	. . . . . . . . . 10
18	17	bibi2d 318	. . . . . . . . 9
19	18	albidv 1713	. . . . . . . 8
20	19	notbid 294	. . . . . . 7
21	16, 20	dvelim 2079	. . . . . 6
22	3	notbid 294	. . . . . . 7
23	22	a1i 11	. . . . . 6
24	15, 21, 23	cbv2h 2019	. . . . 5
25	8, 24	syl 16	. . . 4
26	25	notbid 294	. . 3
27		df-ex 1613	. . 3
28		df-ex 1613	. . 3
29	26, 27, 28	3bitr4g 288	. 2
30	5, 29	pm2.61i 164	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  A.wal 1393  E.wex 1612

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617