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Theorem rel0 5132
Description: The empty set is a relation. (Contributed by NM, 26-Apr-1998.)
Assertion
Ref Expression
rel0

Proof of Theorem rel0
StepHypRef Expression
1 0ss 3814 . 2
2 df-rel 5011 . 2
31, 2mpbir 209 1
Colors of variables: wff setvar class
Syntax hints:   cvv 3109  C_wss 3475   c0 3784  X.cxp 5002  Relwrel 5009
This theorem is referenced by:  reldm0  5225  cnv0  5414  cnveq0  5468  co02  5526  co01  5527  tpos0  7004  0we1  7175  0er  7365  canthwe  9050  dibvalrel  36890  dicvalrelN  36912  dihvalrel  37006
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-rel 5011
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