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Theorem br0 4493
Description: The empty binary relation never holds. (Contributed by NM, 23-Aug-2018.)
Assertion
Ref Expression
br0  |-  -.  A (/) B

Proof of Theorem br0
StepHypRef Expression
1 noel 3789 . 2  |-  -.  <. A ,  B >.  e.  (/)
2 df-br 4448 . 2  |-  ( A
(/) B  <->  <. A ,  B >.  e.  (/) )
31, 2mtbir 299 1  |-  -.  A (/) B
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    e. wcel 1767   (/)c0 3785   <.cop 4033   class class class wbr 4447
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-dif 3479  df-nul 3786  df-br 4448
This theorem is referenced by:  sbcbr  4500  meet0  15627  join0  15628
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