Description: Negation of subclass relationship. (Contributed by Glauco Siliprandi, 3-Mar-2021)
Ref | Expression | ||
---|---|---|---|
Assertion | nssrex | ⊢ ( ¬ 𝐴 ⊆ 𝐵 ↔ ∃ 𝑥 ∈ 𝐴 ¬ 𝑥 ∈ 𝐵 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nss | ⊢ ( ¬ 𝐴 ⊆ 𝐵 ↔ ∃ 𝑥 ( 𝑥 ∈ 𝐴 ∧ ¬ 𝑥 ∈ 𝐵 ) ) | |
2 | df-rex | ⊢ ( ∃ 𝑥 ∈ 𝐴 ¬ 𝑥 ∈ 𝐵 ↔ ∃ 𝑥 ( 𝑥 ∈ 𝐴 ∧ ¬ 𝑥 ∈ 𝐵 ) ) | |
3 | 1 2 | bitr4i | ⊢ ( ¬ 𝐴 ⊆ 𝐵 ↔ ∃ 𝑥 ∈ 𝐴 ¬ 𝑥 ∈ 𝐵 ) |