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Theorem rel0 5276
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 4005 . 2 ∅ ⊆ (V × V)
2 df-rel 5150 . 2 (Rel ∅ ↔ ∅ ⊆ (V × V))
31, 2mpbir 221 1 Rel ∅
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3231  wss 3607  c0 3948   × cxp 5141  Rel wrel 5148
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-dif 3610  df-in 3614  df-ss 3621  df-nul 3949  df-rel 5150
This theorem is referenced by:  reldm0  5375  cnv0OLD  5571  cnveq0  5626  co02  5687  co01  5688  tpos0  7427  0we1  7631  0er  7824  canthwe  9511  dibvalrel  36769  dicvalrelN  36791  dihvalrel  36885
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