Description: A class is not equal to any of its elements. (Contributed by AV, 14-Jun-2022)
Ref | Expression | ||
---|---|---|---|
Assertion | elneq | ⊢ ( 𝐴 ∈ 𝐵 → 𝐴 ≠ 𝐵 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elirr | ⊢ ¬ 𝐵 ∈ 𝐵 | |
2 | nelelne | ⊢ ( ¬ 𝐵 ∈ 𝐵 → ( 𝐴 ∈ 𝐵 → 𝐴 ≠ 𝐵 ) ) | |
3 | 1 2 | ax-mp | ⊢ ( 𝐴 ∈ 𝐵 → 𝐴 ≠ 𝐵 ) |