Metamath Proof Explorer


Definition df-disjss

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 }

Detailed syntax breakdown

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 }