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Theorem brlb 30722
 Description: Binary relationship form of the lower bound functor. (Contributed by Scott Fenton, 3-May-2018.)
Hypotheses
Ref Expression
brub.1
brub.2
Assertion
Ref Expression
brlb LB
Distinct variable groups:   ,   ,   ,

Proof of Theorem brlb
StepHypRef Expression
1 df-lb 30643 . . 3 LB UB
21breqi 4408 . 2 LB UB
3 brub.1 . . 3
4 brub.2 . . 3
53, 4brub 30721 . 2 UB
6 vex 3048 . . . 4
76, 4brcnv 5017 . . 3
87ralbii 2819 . 2
92, 5, 83bitri 275 1 LB
 Colors of variables: wff setvar class Syntax hints:   wb 188   wcel 1887  wral 2737  cvv 3045   class class class wbr 4402  ccnv 4833  UBcub 30618  LBclb 30619 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-9 1896  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431  ax-sep 4525  ax-nul 4534  ax-pr 4639 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 987  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-eu 2303  df-mo 2304  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ne 2624  df-ral 2742  df-rex 2743  df-rab 2746  df-v 3047  df-dif 3407  df-un 3409  df-in 3411  df-ss 3418  df-nul 3732  df-if 3882  df-sn 3969  df-pr 3971  df-op 3975  df-br 4403  df-opab 4462  df-eprel 4745  df-xp 4840  df-cnv 4842  df-co 4843  df-ub 30642  df-lb 30643 This theorem is referenced by: (None)
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