Description: A class cannot be an element of one of its elements. (Contributed by AV, 14-Jun-2022)
Ref | Expression | ||
---|---|---|---|
Assertion | elnel | ⊢ ( 𝐴 ∈ 𝐵 → 𝐵 ∉ 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elnotel | ⊢ ( 𝐴 ∈ 𝐵 → ¬ 𝐵 ∈ 𝐴 ) | |
2 | df-nel | ⊢ ( 𝐵 ∉ 𝐴 ↔ ¬ 𝐵 ∈ 𝐴 ) | |
3 | 1 2 | sylibr | ⊢ ( 𝐴 ∈ 𝐵 → 𝐵 ∉ 𝐴 ) |