Theorem rel0 4844

Description: The empty set is a relation. (Contributed by NM, 26-Apr-1998.)

Assertion

Ref	Expression
rel0	|- Rel (/)

Proof of Theorem rel0

Step	Hyp	Ref	Expression
1		0ss 3530	. 2 |- (/) C_ ( _V X. _V )
2		df-rel 4726	. 2 |- ( Rel (/) <-> (/) C_ ( _V X. _V ) )
3	1, 2	mpbir 146	1 |- Rel (/)

Syntax hints:   _Vcvv 2799   C_ wss 3197   (/)c0 3491   X. cxp 4717   Rel wrel 4724

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 617  ax-in2 618  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-dif 3199  df-in 3203  df-ss 3210  df-nul 3492  df-rel 4726

This theorem is referenced by:  reldm0  4941  cnv0  5132  cnveq0  5185  co02  5242  co01  5243  tpos0  6420  0er  6714