Description: The empty set doesn't belong to a filter. (Contributed by FL, 20-Jul-2007) (Revised by Mario Carneiro, 28-Jul-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | 0nelfil | ⊢ ( 𝐹 ∈ ( Fil ‘ 𝑋 ) → ¬ ∅ ∈ 𝐹 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | filfbas | ⊢ ( 𝐹 ∈ ( Fil ‘ 𝑋 ) → 𝐹 ∈ ( fBas ‘ 𝑋 ) ) | |
2 | 0nelfb | ⊢ ( 𝐹 ∈ ( fBas ‘ 𝑋 ) → ¬ ∅ ∈ 𝐹 ) | |
3 | 1 2 | syl | ⊢ ( 𝐹 ∈ ( Fil ‘ 𝑋 ) → ¬ ∅ ∈ 𝐹 ) |