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Mirrors > Home > MPE Home > Th. List > issoi | Structured version Visualization version Unicode version |
Description: An irreflexive, transitive, linear relation is a strict ordering. (Contributed by NM, 21-Jan-1996.) (Revised by Mario Carneiro, 9-Jul-2014.) |
Ref | Expression |
---|---|
issoi.1 | |
issoi.2 | |
issoi.3 |
Ref | Expression |
---|---|
issoi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | issoi.1 | . . . . 5 | |
2 | 1 | adantl 482 | . . . 4 |
3 | issoi.2 | . . . . 5 | |
4 | 3 | adantl 482 | . . . 4 |
5 | 2, 4 | ispod 5043 | . . 3 |
6 | issoi.3 | . . . 4 | |
7 | 6 | adantl 482 | . . 3 |
8 | 5, 7 | issod 5065 | . 2 |
9 | 8 | trud 1493 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wa 384 w3o 1036 w3a 1037 wtru 1484 wcel 1990 class class class wbr 4653 wor 5034 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 |
This theorem depends on definitions: df-bi 197 df-an 386 df-3an 1039 df-tru 1486 df-ral 2917 df-po 5035 df-so 5036 |
This theorem is referenced by: isso2i 5067 ltsopr 9854 sltsolem1 31826 |
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