Theorem disjrel 39742

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 39702	. 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 5650  Rel wrel 5656   ≀ ccoss 39095   CnvRefRel wcnvrefrel 39104   Disj wdisjALTV 39131

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 39702

This theorem is used by:  disjlem18  39815  disjdmqsss  39817  disjdmqscossss  39818