Theorem br0 4066

Description: The empty binary relation never holds. (Contributed by NM, 23-Aug-2018.)

Assertion

Ref	Expression
br0	|- -. A (/) B

Proof of Theorem br0

Step	Hyp	Ref	Expression
1		noel 3441	. 2 |- -. <. A , B >. e. (/)
2		df-br 4019	. 2 |- ( A (/) B <-> <. A , B >. e. (/) )
3	1, 2	mtbir 672	1 |- -. A (/) B

Syntax hints:   -. wn 3   e. wcel 2160   (/)c0 3437   <.cop 3610   class class class wbr 4018

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-dif 3146  df-nul 3438  df-br 4019

This theorem is referenced by: (None)