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Theorem so2nr 4049
 Description: A strict order relation has no 2-cycle loops. (Contributed by NM, 21-Jan-1996.)
Assertion
Ref Expression
so2nr ((𝑅 Or A (B A 𝐶 A)) → ¬ (B𝑅𝐶 𝐶𝑅B))

Proof of Theorem so2nr
StepHypRef Expression
1 sopo 4041 . 2 (𝑅 Or A𝑅 Po A)
2 po2nr 4037 . 2 ((𝑅 Po A (B A 𝐶 A)) → ¬ (B𝑅𝐶 𝐶𝑅B))
31, 2sylan 267 1 ((𝑅 Or A (B A 𝐶 A)) → ¬ (B𝑅𝐶 𝐶𝑅B))
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 97   ∈ wcel 1390   class class class wbr 3755   Po wpo 4022   Or wor 4023 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-po 4024  df-iso 4025 This theorem is referenced by:  sotricim  4051  cauappcvgprlemdisj  6623  cauappcvgprlemladdru  6628  cauappcvgprlemladdrl  6629  caucvgprlemnbj  6638  ltnsym2  6905
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