Hilbert Space Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  HSE Home  >  Th. List  >  cvbr Unicode version

Theorem cvbr 22862
 Description: Binary relation expressing covers , which means that is larger than and there is nothing in between. Definition 3.2.18 of [PtakPulmannova] p. 68. (Contributed by NM, 4-Jun-2004.) (New usage is discouraged.)
Assertion
Ref Expression
cvbr
Distinct variable groups:   ,   ,

Proof of Theorem cvbr
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eleq1 2343 . . . . 5
21anbi1d 685 . . . 4
3 psseq1 3263 . . . . 5
4 psseq1 3263 . . . . . . . 8
54anbi1d 685 . . . . . . 7
65rexbidv 2564 . . . . . 6
76notbid 285 . . . . 5
83, 7anbi12d 691 . . . 4
92, 8anbi12d 691 . . 3
10 eleq1 2343 . . . . 5
1110anbi2d 684 . . . 4
12 psseq2 3264 . . . . 5
13 psseq2 3264 . . . . . . . 8
1413anbi2d 684 . . . . . . 7
1514rexbidv 2564 . . . . . 6
1615notbid 285 . . . . 5
1712, 16anbi12d 691 . . . 4
1811, 17anbi12d 691 . . 3
19 df-cv 22859 . . 3
209, 18, 19brabg 4284 . 2
2120bianabs 850 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wa 358   wceq 1623   wcel 1684  wrex 2544   wpss 3153   class class class wbr 4023  cch 21509   ccv 21544 This theorem is referenced by:  cvbr2  22863  cvcon3  22864  cvpss  22865  cvnbtwn  22866 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-pss 3168  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-cv 22859
 Copyright terms: Public domain W3C validator