Description: A nonempty intersection. (Contributed by Glauco Siliprandi, 24-Dec-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | inn0 | ⊢ ( ( 𝐴 ∩ 𝐵 ) ≠ ∅ ↔ ∃ 𝑥 ∈ 𝐴 𝑥 ∈ 𝐵 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv | ⊢ Ⅎ 𝑥 𝐴 | |
2 | nfcv | ⊢ Ⅎ 𝑥 𝐵 | |
3 | 1 2 | inn0f | ⊢ ( ( 𝐴 ∩ 𝐵 ) ≠ ∅ ↔ ∃ 𝑥 ∈ 𝐴 𝑥 ∈ 𝐵 ) |