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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 38685 | . 2 ⊢ Disjs = ( Disjss ∩ Rels ) | |
2 | df-disjss 38684 | . 2 ⊢ Disjss = {𝑟 ∣ ≀ ◡𝑟 ∈ CnvRefRels } | |
3 | 1, 2 | abeqin 38233 | 1 ⊢ Disjs = {𝑟 ∈ Rels ∣ ≀ ◡𝑟 ∈ CnvRefRels } |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1536 ∈ wcel 2105 {crab 3432 ◡ccnv 5687 ≀ ccoss 38161 Rels crels 38163 CnvRefRels ccnvrefrels 38169 Disjss cdisjss 38193 Disjs cdisjs 38194 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-8 2107 ax-9 2115 ax-ext 2705 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1539 df-ex 1776 df-sb 2062 df-clab 2712 df-cleq 2726 df-clel 2813 df-rab 3433 df-v 3479 df-in 3969 df-disjss 38684 df-disjs 38685 |
This theorem is referenced by: dfdisjs2 38690 eldisjs 38703 |
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