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Theorem rel0 5639
 Description: The empty set is a relation. (Contributed by NM, 26-Apr-1998.)
Assertion
Ref Expression
rel0 Rel ∅

Proof of Theorem rel0
StepHypRef Expression
1 0ss 4306 . 2 ∅ ⊆ (V × V)
2 df-rel 5529 . 2 (Rel ∅ ↔ ∅ ⊆ (V × V))
31, 2mpbir 234 1 Rel ∅
 Colors of variables: wff setvar class Syntax hints:  Vcvv 3441   ⊆ wss 3882  ∅c0 4245   × cxp 5520  Rel wrel 5527 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-dif 3885  df-in 3889  df-ss 3899  df-nul 4246  df-rel 5529 This theorem is referenced by:  relsnb  5642  reldm0  5767  cnveq0  6024  co02  6085  co01  6086  tpos0  7920  0we1  8129  0er  8324  canthwe  10077  relexpreld  14408  disjALTV0  36211  dibvalrel  38526  dicvalrelN  38548  dihvalrel  38642
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