Theorem isso2i 4837

Description: Deduce strict ordering from its properties. (Contributed by NM, 29-Jan-1996.) (Revised by Mario Carneiro, 9-Jul-2014.)

Hypotheses

Ref	Expression
isso2i.1
isso2i.2

Assertion

Ref	Expression
isso2i

Distinct variable groups:   ,,,   ,,,

Proof of Theorem isso2i

Step	Hyp	Ref	Expression
1		equid 1791	. . . . 5
2	1	orci 390	. . . 4
3		eleq1 2529	. . . . . . 7
4	3	anbi2d 703	. . . . . 6
5		equequ2 1799	. . . . . . . 8
6		breq1 4455	. . . . . . . 8
7	5, 6	orbi12d 709	. . . . . . 7
8		breq2 4456	. . . . . . . 8
9	8	notbid 294	. . . . . . 7
10	7, 9	bibi12d 321	. . . . . 6
11	4, 10	imbi12d 320	. . . . 5
12		isso2i.1	. . . . . 6
13	12	con2bid 329	. . . . 5
14	11, 13	chvarv 2014	. . . 4
15	2, 14	mpbii 211	. . 3
16	15	anidms 645	. 2
17		isso2i.2	. 2
18	13	biimprd 223	. . 3
19		3orass 976	. . . 4
20		df-or 370	. . . 4
21	19, 20	bitri 249	. . 3
22	18, 21	sylibr 212	. 2
23	16, 17, 22	issoi 4836	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369  \/w3o 972  /\w3a 973  e.wcel 1818   class class class wbr 4452  Orwor 4804

This theorem is referenced by:  ltsonq  9368  ltsosr  9492  ltso  9686  xrltso  11376

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  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-po 4805  df-so 4806