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Theorem sotr2 4834
Description: A transitivity relation. (Read and implies .) (Contributed by Mario Carneiro, 10-May-2013.)
Assertion
Ref Expression
sotr2

Proof of Theorem sotr2
StepHypRef Expression
1 sotric 4831 . . . . . 6
21ancom2s 802 . . . . 5
323adantr3 1157 . . . 4
43con2bid 329 . . 3
5 breq1 4455 . . . . . 6
65biimpd 207 . . . . 5
76a1i 11 . . . 4
8 sotr 4827 . . . . 5
98expd 436 . . . 4
107, 9jaod 380 . . 3
114, 10sylbird 235 . 2
1211impd 431 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369  /\w3a 973  =wceq 1395  e.wcel 1818   class class class wbr 4452  Orwor 4804
This theorem is referenced by:  erdszelem8  28642
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-po 4805  df-so 4806
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