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Theorem lcvnbtwn 29897
 Description: The covers relation implies no in-betweenness. (cvnbtwn 23794 analog.) (Contributed by NM, 7-Jan-2015.)
Hypotheses
Ref Expression
lcvnbtwn.s
lcvnbtwn.c L
lcvnbtwn.w
lcvnbtwn.r
lcvnbtwn.t
lcvnbtwn.u
lcvnbtwn.d
Assertion
Ref Expression
lcvnbtwn

Proof of Theorem lcvnbtwn
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 lcvnbtwn.d . . . 4
2 lcvnbtwn.s . . . . 5
3 lcvnbtwn.c . . . . 5 L
4 lcvnbtwn.w . . . . 5
5 lcvnbtwn.r . . . . 5
6 lcvnbtwn.t . . . . 5
72, 3, 4, 5, 6lcvbr 29893 . . . 4
81, 7mpbid 203 . . 3
98simprd 451 . 2
10 lcvnbtwn.u . . 3
11 psseq2 3437 . . . . 5
12 psseq1 3436 . . . . 5
1311, 12anbi12d 693 . . . 4
1413rspcev 3054 . . 3
1510, 14sylan 459 . 2
169, 15mtand 642 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360   wceq 1653   wcel 1726  wrex 2708   wpss 3323   class class class wbr 4215  cfv 5457  clss 16013   L clcv 29890 This theorem is referenced by:  lcvntr  29898  lcvnbtwn2  29899  lcvnbtwn3  29900 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pow 4380  ax-pr 4406  ax-un 4704 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-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-pss 3338  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-opab 4270  df-mpt 4271  df-id 4501  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-iota 5421  df-fun 5459  df-fv 5465  df-lcv 29891
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