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Theorem rel0 5214
 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 3950 . 2 ∅ ⊆ (V × V)
2 df-rel 5091 . 2 (Rel ∅ ↔ ∅ ⊆ (V × V))
31, 2mpbir 221 1 Rel ∅
 Colors of variables: wff setvar class Syntax hints:  Vcvv 3190   ⊆ wss 3560  ∅c0 3897   × cxp 5082  Rel wrel 5089 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3192  df-dif 3563  df-in 3567  df-ss 3574  df-nul 3898  df-rel 5091 This theorem is referenced by:  reldm0  5313  cnv0OLD  5505  cnveq0  5560  co02  5618  co01  5619  tpos0  7342  0we1  7546  0er  7740  0erOLD  7741  canthwe  9433  dibvalrel  35971  dicvalrelN  35993  dihvalrel  36087
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