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Theorem cvbr2 23774
 Description: Binary relation expressing covers . Definition of covers in [Kalmbach] p. 15. (Contributed by NM, 9-Jun-2004.) (New usage is discouraged.)
Assertion
Ref Expression
cvbr2
Distinct variable groups:   ,   ,

Proof of Theorem cvbr2
StepHypRef Expression
1 cvbr 23773 . 2
2 iman 414 . . . . . 6
3 anass 631 . . . . . . 7
4 dfpss2 3424 . . . . . . . 8
54anbi2i 676 . . . . . . 7
63, 5bitr4i 244 . . . . . 6
72, 6xchbinx 302 . . . . 5
87ralbii 2721 . . . 4
9 ralnex 2707 . . . 4
108, 9bitri 241 . . 3
1110anbi2i 676 . 2
121, 11syl6bbr 255 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  wral 2697  wrex 2698   wss 3312   wpss 3313   class class class wbr 4204  cch 22420   ccv 22455 This theorem is referenced by:  spansncv2  23784  elat2  23831 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-pss 3328  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-cv 23770
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