Description: Any set is a converse subset of itself. (Contributed by Peter Mazsa, 9-Jun-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | brcnvssrid | ⊢ ( 𝐴 ∈ 𝑉 → 𝐴 ◡ S 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssid | ⊢ 𝐴 ⊆ 𝐴 | |
2 | brcnvssr | ⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 ◡ S 𝐴 ↔ 𝐴 ⊆ 𝐴 ) ) | |
3 | 1 2 | mpbiri | ⊢ ( 𝐴 ∈ 𝑉 → 𝐴 ◡ S 𝐴 ) |