Metamath Proof Explorer


Theorem bj-n0i

Description: Inference associated with n0 . Shortens 2ndcdisj (2888>2878), notsep (264>253). (Contributed by BJ, 22-Apr-2019)

Ref Expression
Hypothesis bj-n0i.1 ⊢ A ≠ ∅
Assertion bj-n0i ⊢ ∃ x x ∈ A

Proof

Step Hyp Ref Expression
1 bj-n0i.1 ⊢ A ≠ ∅
2 n0 ⊢ A ≠ ∅ ↔ ∃ x x ∈ A
3 1 2 mpbi ⊢ ∃ x x ∈ A