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Theorem issod 4536
 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
issod.1
issod.2
Assertion
Ref Expression
issod
Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem issod
StepHypRef Expression
1 issod.1 . 2
2 issod.2 . . 3
32ralrimivva 2800 . 2
4 df-so 4507 . 2
51, 3, 4sylanbrc 647 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   w3o 936   wcel 1726  wral 2707   class class class wbr 4215   wpo 4504   wor 4505 This theorem is referenced by:  issoi  4537  swoso  6939  wemapso2lem  7522  socnv  25393 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555  df-ral 2712  df-so 4507
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