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Theorem issod 4820
 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 2864 . 2
4 df-so 4791 . 2
51, 3, 4sylanbrc 664 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   w3o 973   wcel 1804  wral 2793   class class class wbr 4437   wpo 4788   wor 4789 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691 This theorem depends on definitions:  df-bi 185  df-an 371  df-ral 2798  df-so 4791 This theorem is referenced by:  issoi  4821  swoso  7344  wemapsolem  7978  legso  23857  socnv  29169  fin2so  30015
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