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Theorem cvnbtwn2 23792
 Description: The covers relation implies no in-betweenness. (Contributed by NM, 12-Jun-2004.) (New usage is discouraged.)
Assertion
Ref Expression
cvnbtwn2

Proof of Theorem cvnbtwn2
StepHypRef Expression
1 cvnbtwn 23791 . 2
2 iman 415 . . 3
3 anass 632 . . . . 5
4 dfpss2 3434 . . . . . 6
54anbi2i 677 . . . . 5
63, 5bitr4i 245 . . . 4
76notbii 289 . . 3
82, 7bitr2i 243 . 2
91, 8syl6ib 219 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360   w3a 937   wceq 1653   wcel 1726   wss 3322   wpss 3323   class class class wbr 4214  cch 22434   ccv 22469 This theorem is referenced by:  cvati  23871  cvexchlem  23873  atexch  23886 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-pss 3338  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4215  df-opab 4269  df-cv 23784
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