Theorem disjrel 38686

Description: Disjoint relation is a relation. (Contributed by Peter Mazsa, 15-Sep-2021.)

Assertion

Ref	Expression
disjrel	⊢ ( Disj 𝑅 → Rel 𝑅)

Proof of Theorem disjrel

Step	Hyp	Ref	Expression
1		df-disjALTV 38661	. 2 ⊢ ( Disj 𝑅 ↔ ( CnvRefRel ≀ ◡𝑅 ∧ Rel 𝑅))
2	1	simprbi 496	1 ⊢ ( Disj 𝑅 → Rel 𝑅)

Syntax hints:   → wi 4  ^◡ccnv 5699  Rel wrel 5705   ≀ ccoss 38135   CnvRefRel wcnvrefrel 38144   Disj wdisjALTV 38169

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-disjALTV 38661

This theorem is referenced by:  disjlem18  38756  disjdmqsss  38758  disjdmqscossss  38759