Theorem br0 4092

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 3464	. 2 |- -. <. A , B >. e. (/)
2		df-br 4045	. 2 |- ( A (/) B <-> <. A , B >. e. (/) )
3	1, 2	mtbir 673	1 |- -. A (/) B

Syntax hints:   -. wn 3   e. wcel 2176   (/)c0 3460   <.cop 3636   class class class wbr 4044

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-dif 3168  df-nul 3461  df-br 4045

This theorem is referenced by: (None)