Description: Alternate definition of the class of disjoints. (Contributed by Peter Mazsa, 5-Sep-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | dfdisjs2 | |- Disjs = { r e. Rels | ,~ `' r C_ _I } |
Step | Hyp | Ref | Expression |
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1 | dfdisjs | |- Disjs = { r e. Rels | ,~ `' r e. CnvRefRels } |
|
2 | cosselcnvrefrels2 | |- ( ,~ `' r e. CnvRefRels <-> ( ,~ `' r C_ _I /\ ,~ `' r e. Rels ) ) |
|
3 | cosscnvelrels | |- ( r e. Rels -> ,~ `' r e. Rels ) |
|
4 | 3 | biantrud | |- ( r e. Rels -> ( ,~ `' r C_ _I <-> ( ,~ `' r C_ _I /\ ,~ `' r e. Rels ) ) ) |
5 | 2 4 | bitr4id | |- ( r e. Rels -> ( ,~ `' r e. CnvRefRels <-> ,~ `' r C_ _I ) ) |
6 | 1 5 | rabimbieq | |- Disjs = { r e. Rels | ,~ `' r C_ _I } |