Description: Define the class of all disjoint sets (but not necessarily disjoint relations, cf. df-disjs ). It is used only by df-disjs . (Contributed by Peter Mazsa, 17-Jul-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | df-disjss | ⊢ Disjss = { 𝑥 ∣ ≀ ◡ 𝑥 ∈ CnvRefRels } |
Step | Hyp | Ref | Expression |
---|---|---|---|
0 | cdisjss | ⊢ Disjss | |
1 | vx | ⊢ 𝑥 | |
2 | 1 | cv | ⊢ 𝑥 |
3 | 2 | ccnv | ⊢ ◡ 𝑥 |
4 | 3 | ccoss | ⊢ ≀ ◡ 𝑥 |
5 | ccnvrefrels | ⊢ CnvRefRels | |
6 | 4 5 | wcel | ⊢ ≀ ◡ 𝑥 ∈ CnvRefRels |
7 | 6 1 | cab | ⊢ { 𝑥 ∣ ≀ ◡ 𝑥 ∈ CnvRefRels } |
8 | 0 7 | wceq | ⊢ Disjss = { 𝑥 ∣ ≀ ◡ 𝑥 ∈ CnvRefRels } |