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Metamath Proof Explorer

Theorem inn0

Description: A nonempty intersection. (Contributed by Glauco Siliprandi, 24-Dec-2020)

Ref Expression
Assertion inn0 ⊢ A ∩ B ≠ ∅ ↔ ∃ x ∈ A x ∈ B

Proof

Step Hyp Ref Expression
1 nfcv ⊢ Ⅎ _ x A
2 nfcv ⊢ Ⅎ _ x B
3 1 2 inn0f ⊢ A ∩ B ≠ ∅ ↔ ∃ x ∈ A x ∈ B