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Theorem rel0 5809
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 4400 . 2 ∅ ⊆ (V × V)
2 df-rel 5692 . 2 (Rel ∅ ↔ ∅ ⊆ (V × V))
31, 2mpbir 231 1 Rel ∅
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3480  wss 3951  c0 4333   × cxp 5683  Rel wrel 5690
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-dif 3954  df-ss 3968  df-nul 4334  df-rel 5692
This theorem is referenced by:  relsnb  5812  reldm0  5938  cnveq0  6217  co02  6280  co01  6281  tpos0  8281  0we1  8544  0er  8783  canthwe  10691  relexpreld  15079  disjALTV0  38755  dibvalrel  41165  dicvalrelN  41187  dihvalrel  41281
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