Metamath Proof Explorer
Description: An irreflexive, transitive, linear relation is a strict ordering.
(Contributed by NM, 21-Jan-1996) (Revised by Mario Carneiro, 9-Jul-2014)
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Ref |
Expression |
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Hypotheses |
issoi.1 |
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|
issoi.2 |
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|
issoi.3 |
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|
Assertion |
issoi |
|
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
issoi.1 |
|
2 |
|
issoi.2 |
|
3 |
|
issoi.3 |
|
4 |
1
|
adantl |
|
5 |
2
|
adantl |
|
6 |
4 5
|
ispod |
|
7 |
3
|
adantl |
|
8 |
6 7
|
issod |
|
9 |
8
|
mptru |
|