![]() |
Mathbox for Peter Mazsa |
< Previous
Next >
Nearby theorems |
|
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 37216 | . 2 ⊢ Disjs = ( Disjss ∩ Rels ) | |
2 | df-disjss 37215 | . 2 ⊢ Disjss = {𝑟 ∣ ≀ ◡𝑟 ∈ CnvRefRels } | |
3 | 1, 2 | abeqin 36762 | 1 ⊢ Disjs = {𝑟 ∈ Rels ∣ ≀ ◡𝑟 ∈ CnvRefRels } |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 ∈ wcel 2107 {crab 3406 ◡ccnv 5636 ≀ ccoss 36684 Rels crels 36686 CnvRefRels ccnvrefrels 36692 Disjss cdisjss 36716 Disjs cdisjs 36717 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-rab 3407 df-v 3449 df-in 3921 df-disjss 37215 df-disjs 37216 |
This theorem is referenced by: dfdisjs2 37221 eldisjs 37234 |
Copyright terms: Public domain | W3C validator |