Theorem disjrel 39578

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 39538	. 2 ⊢ ( Disj 𝑅 ↔ ( CnvRefRel ≀ ◡𝑅 ∧ Rel 𝑅))
2	1	simprbi 503	1 ⊢ ( Disj 𝑅 → Rel 𝑅)

This proof depends on syntax axioms:   → wi 4  ^◡ccnv 5654  Rel wrel 5660   ≀ ccoss 38931   CnvRefRel wcnvrefrel 38940   Disj wdisjALTV 38967

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-disjALTV 39538

This theorem is used by:  disjlem18  39651  disjdmqsss  39653  disjdmqscossss  39654