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Theorem rel0 5151
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 3919 . 2 ∅ ⊆ (V × V)
2 df-rel 5031 . 2 (Rel ∅ ↔ ∅ ⊆ (V × V))
31, 2mpbir 219 1 Rel ∅
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3168  wss 3535  c0 3869   × cxp 5022  Rel wrel 5029
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1711  ax-4 1726  ax-5 1825  ax-6 1873  ax-7 1920  ax-10 2004  ax-11 2019  ax-12 2031  ax-13 2228  ax-ext 2585
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1866  df-clab 2592  df-cleq 2598  df-clel 2601  df-nfc 2735  df-v 3170  df-dif 3538  df-in 3542  df-ss 3549  df-nul 3870  df-rel 5031
This theorem is referenced by:  reldm0  5247  cnv0  5437  cnveq0  5491  co02  5548  co01  5549  tpos0  7242  0we1  7446  0er  7640  0erOLD  7641  canthwe  9325  dibvalrel  35269  dicvalrelN  35291  dihvalrel  35385
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