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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 38705 | . 2 ⊢ Disjs = ( Disjss ∩ Rels ) | |
| 2 | df-disjss 38704 | . 2 ⊢ Disjss = {𝑟 ∣ ≀ ◡𝑟 ∈ CnvRefRels } | |
| 3 | 1, 2 | abeqin 38253 | 1 ⊢ Disjs = {𝑟 ∈ Rels ∣ ≀ ◡𝑟 ∈ CnvRefRels } |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 ∈ wcel 2108 {crab 3436 ◡ccnv 5684 ≀ ccoss 38182 Rels crels 38184 CnvRefRels ccnvrefrels 38190 Disjss cdisjss 38214 Disjs cdisjs 38215 |
| 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 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-rab 3437 df-v 3482 df-in 3958 df-disjss 38704 df-disjs 38705 |
| This theorem is referenced by: dfdisjs2 38710 eldisjs 38723 |
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