Description: A proper subclass does not include the other class. (Contributed by Glauco Siliprandi, 26-Jun-2021)
Ref | Expression | ||
---|---|---|---|
Hypothesis | pssnssi.1 | ⊢ 𝐴 ⊊ 𝐵 | |
Assertion | pssnssi | ⊢ ¬ 𝐵 ⊆ 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pssnssi.1 | ⊢ 𝐴 ⊊ 𝐵 | |
2 | dfpss3 | ⊢ ( 𝐴 ⊊ 𝐵 ↔ ( 𝐴 ⊆ 𝐵 ∧ ¬ 𝐵 ⊆ 𝐴 ) ) | |
3 | 1 2 | mpbi | ⊢ ( 𝐴 ⊆ 𝐵 ∧ ¬ 𝐵 ⊆ 𝐴 ) |
4 | 3 | simpri | ⊢ ¬ 𝐵 ⊆ 𝐴 |