Theorem bj-n0i 36886

Description: Inference associated with n0 4333. Shortens 2ndcdisj 23409 (2888>2878), notzfaus 5343 (264>253). (Contributed by BJ, 22-Apr-2019.)

Hypothesis

Ref	Expression
bj-n0i.1	⊢ 𝐴 ≠ ∅

Assertion

Ref	Expression
bj-n0i	⊢ ∃𝑥 𝑥 ∈ 𝐴

Distinct variable group:   𝑥,𝐴

Proof of Theorem bj-n0i

Step	Hyp	Ref	Expression
1		bj-n0i.1	. 2 ⊢ 𝐴 ≠ ∅
2		n0 4333	. 2 ⊢ (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴)
3	1, 2	mpbi 230	1 ⊢ ∃𝑥 𝑥 ∈ 𝐴

Syntax hints:  ∃wex 1778   ∈ wcel 2107   ≠ wne 2931  ∅c0 4313

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-9 2117  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-ne 2932  df-dif 3934  df-nul 4314

This theorem is referenced by: (None)