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Mirrors > Home > MPE Home > Th. List > Mathboxes > dfdisjs | Structured version Visualization version GIF version |
Description: Alternate definition of the class of disjoints. (Contributed by Peter Mazsa, 18-Jul-2021.) |
Ref | Expression |
---|---|
dfdisjs | ⊢ Disjs = {𝑟 ∈ Rels ∣ ≀ ◡𝑟 ∈ CnvRefRels } |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-disjs 35973 | . 2 ⊢ Disjs = ( Disjss ∩ Rels ) | |
2 | df-disjss 35972 | . 2 ⊢ Disjss = {𝑟 ∣ ≀ ◡𝑟 ∈ CnvRefRels } | |
3 | 1, 2 | abeqin 35550 | 1 ⊢ Disjs = {𝑟 ∈ Rels ∣ ≀ ◡𝑟 ∈ CnvRefRels } |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1536 ∈ wcel 2113 {crab 3141 ◡ccnv 5551 ≀ ccoss 35489 Rels crels 35491 CnvRefRels ccnvrefrels 35497 Disjss cdisjss 35521 Disjs cdisjs 35522 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 ax-8 2115 ax-9 2123 ax-10 2144 ax-11 2160 ax-12 2176 ax-ext 2792 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1539 df-ex 1780 df-nf 1784 df-sb 2069 df-clab 2799 df-cleq 2813 df-clel 2892 df-nfc 2962 df-rab 3146 df-v 3495 df-in 3940 df-disjss 35972 df-disjs 35973 |
This theorem is referenced by: dfdisjs2 35978 eldisjs 35991 |
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