Theorem bj-n0i 37127

Description: Inference associated with n0 4306. Shortens 2ndcdisj 23404 (2888>2878), notzfaus 5309 (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 4306	. 2 ⊢ (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴)
3	1, 2	mpbi 230	1 ⊢ ∃𝑥 𝑥 ∈ 𝐴

Syntax hints:  ∃wex 1781   ∈ wcel 2114   ≠ wne 2933  ∅c0 4286

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-9 2124  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-ne 2934  df-dif 3905  df-nul 4287

This theorem is referenced by: (None)