Theorem rel0 3329

Description: The empty set is a relation.

Assertion

Ref	Expression
rel0	⊢ Rel ∅

Proof of Theorem rel0

Step	Hyp	Ref	Expression
1		0ss 2353	. 2 ⊢ ∅ ⊆ (V × V)
2		df-rel 3242	. 2 ⊢ (Rel ∅ ↔ ∅ ⊆ (V × V))
3	1, 2	mpbir 197	1 ⊢ Rel ∅

Syntax hints:  Vcvv 1858   ⊆ wss 2098  ∅c0 2331   × cxp 3225  Rel wrel 3232

This theorem is referenced by:  reldm0 3388  intirr 3498  cnv0 3503  co02 3565  co01 3566  fn0 3662  empos 10579

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1003  ax-gen 1004  ax-8 1005  ax-10 1007  ax-12 1009  ax-17 1012  ax-4 1014  ax-5o 1016  ax-6o 1019  ax-9o 1164  ax-10o 1182  ax-16 1252  ax-11o 1260  ax-ext 1504

This theorem depends on definitions:  df-bi 154  df-or 231  df-an 232  df-ex 1022  df-sb 1214  df-clab 1510  df-cleq 1515  df-clel 1518  df-v 1859  df-dif 2100  df-in 2102  df-ss 2104  df-nul 2332  df-rel 3242

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