Theorem issoi 4836

Description: An irreflexive, transitive, linear relation is a strict ordering. (Contributed by NM, 21-Jan-1996.) (Revised by Mario Carneiro, 9-Jul-2014.)

Hypotheses

Ref	Expression
issoi.1
issoi.2
issoi.3

Assertion

Ref	Expression
issoi

Distinct variable groups:   ,,,   ,,,

Proof of Theorem issoi

Step	Hyp	Ref	Expression
1		issoi.1	. . . . 5
2	1	adantl 466	. . . 4
3		issoi.2	. . . . 5
4	3	adantl 466	. . . 4
5	2, 4	ispod 4813	. . 3
6		issoi.3	. . . 4
7	6	adantl 466	. . 3
8	5, 7	issod 4835	. 2
9	8	trud 1404	1

Syntax hints:  -.wn 3  ->wi 4  /\wa 369  \/w3o 972  /\w3a 973  wtru 1396  e.wcel 1818   class class class wbr 4452  Orwor 4804

This theorem is referenced by:  isso2i  4837  ltsopr  9431  sltsolem1  29428

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

This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ral 2812  df-po 4805  df-so 4806