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Mathbox for Peter Mazsa |
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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 38208 | . 2 ⊢ Disjs = ( Disjss ∩ Rels ) | |
2 | df-disjss 38207 | . 2 ⊢ Disjss = {𝑟 ∣ ≀ ◡𝑟 ∈ CnvRefRels } | |
3 | 1, 2 | abeqin 37756 | 1 ⊢ Disjs = {𝑟 ∈ Rels ∣ ≀ ◡𝑟 ∈ CnvRefRels } |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 ∈ wcel 2098 {crab 3430 ◡ccnv 5681 ≀ ccoss 37681 Rels crels 37683 CnvRefRels ccnvrefrels 37689 Disjss cdisjss 37713 Disjs cdisjs 37714 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2699 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2706 df-cleq 2720 df-clel 2806 df-rab 3431 df-v 3475 df-in 3956 df-disjss 38207 df-disjs 38208 |
This theorem is referenced by: dfdisjs2 38213 eldisjs 38226 |
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