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Theorem disjrel 37242
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
StepHypRef Expression
1 df-disjALTV 37217 . 2 ( Disj 𝑅 ↔ ( CnvRefRel ≀ 𝑅 ∧ Rel 𝑅))
21simprbi 498 1 ( Disj 𝑅 → Rel 𝑅)
Colors of variables: wff setvar class
Syntax hints:  wi 4  ccnv 5636  Rel wrel 5642  ccoss 36684   CnvRefRel wcnvrefrel 36693   Disj wdisjALTV 36718
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 206  df-an 398  df-disjALTV 37217
This theorem is referenced by:  disjlem18  37312  disjdmqsss  37314  disjdmqscossss  37315
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