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Theorem cvnbtwn4 23749
 Description: The covers relation implies no in-betweenness. Part of proof of Lemma 7.5.1 of [MaedaMaeda] p. 31. (Contributed by NM, 12-Jun-2004.) (New usage is discouraged.)
Assertion
Ref Expression
cvnbtwn4

Proof of Theorem cvnbtwn4
StepHypRef Expression
1 cvnbtwn 23746 . 2
2 iman 414 . . 3
3 an4 798 . . . . 5
4 ioran 477 . . . . . . 7
5 eqcom 2410 . . . . . . . . 9
65notbii 288 . . . . . . . 8
76anbi1i 677 . . . . . . 7
84, 7bitri 241 . . . . . 6
98anbi2i 676 . . . . 5
10 dfpss2 3396 . . . . . 6
11 dfpss2 3396 . . . . . 6
1210, 11anbi12i 679 . . . . 5
133, 9, 123bitr4i 269 . . . 4
1413notbii 288 . . 3
152, 14bitr2i 242 . 2
161, 15syl6ib 218 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wo 358   wa 359   w3a 936   wceq 1649   wcel 1721   wss 3284   wpss 3285   class class class wbr 4176  cch 22389   ccv 22424 This theorem is referenced by:  cvmdi  23784 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389  ax-sep 4294  ax-nul 4302  ax-pr 4367 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2262  df-mo 2263  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-ne 2573  df-rex 2676  df-rab 2679  df-v 2922  df-dif 3287  df-un 3289  df-in 3291  df-ss 3298  df-pss 3300  df-nul 3593  df-if 3704  df-sn 3784  df-pr 3785  df-op 3787  df-br 4177  df-opab 4231  df-cv 23739
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