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Mirrors > Home > MPE Home > Th. List > Mathboxes > disjrel | Structured version Visualization version GIF version |
Description: Disjoint relation is a relation. (Contributed by Peter Mazsa, 15-Sep-2021.) |
Ref | Expression |
---|---|
disjrel | ⊢ ( Disj 𝑅 → Rel 𝑅) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-disjALTV 37217 | . 2 ⊢ ( Disj 𝑅 ↔ ( CnvRefRel ≀ ◡𝑅 ∧ Rel 𝑅)) | |
2 | 1 | simprbi 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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