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Theorem untangtr 25163
 Description: A transitive class is untangled iff its elements are. (Contributed by Scott Fenton, 7-Mar-2011.)
Assertion
Ref Expression
untangtr
Distinct variable group:   ,,

Proof of Theorem untangtr
StepHypRef Expression
1 df-tr 4303 . . . 4
2 ssralv 3407 . . . 4
31, 2sylbi 188 . . 3
4 elequ1 1728 . . . . . . 7
5 elequ2 1730 . . . . . . 7
64, 5bitrd 245 . . . . . 6
76notbid 286 . . . . 5
87cbvralv 2932 . . . 4
9 untuni 25158 . . . 4
108, 9bitri 241 . . 3
113, 10syl6ib 218 . 2
12 untelirr 25157 . . 3
1312ralimi 2781 . 2
1411, 13impbid1 195 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177  wral 2705   wss 3320  cuni 4015   wtr 4302 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-v 2958  df-in 3327  df-ss 3334  df-uni 4016  df-tr 4303
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