Description: Alternate definition of the class of symmetric relations. (Contributed by Peter Mazsa, 20-Jul-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | dfsymrels4 | ⊢ SymRels = { 𝑟 ∈ Rels ∣ ◡ 𝑟 = 𝑟 } |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsymrels2 | ⊢ SymRels = { 𝑟 ∈ Rels ∣ ◡ 𝑟 ⊆ 𝑟 } | |
2 | elrelscnveq | ⊢ ( 𝑟 ∈ Rels → ( ◡ 𝑟 ⊆ 𝑟 ↔ ◡ 𝑟 = 𝑟 ) ) | |
3 | 1 2 | rabimbieq | ⊢ SymRels = { 𝑟 ∈ Rels ∣ ◡ 𝑟 = 𝑟 } |