Theorem bj-n0i 34795

Description: Inference associated with n0 4245. Shortens 2ndcdisj 22219 (2888>2878), notzfaus 5238 (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 4245	. 2 ⊢ (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴)
3	1, 2	mpbi 233	1 ⊢ ∃𝑥 𝑥 ∈ 𝐴

Syntax hints:  ∃wex 1786   ∈ wcel 2114   ≠ wne 2935  ∅c0 4221

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020  ax-9 2124  ax-ext 2711

This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1545  df-fal 1555  df-ex 1787  df-sb 2075  df-clab 2718  df-cleq 2731  df-ne 2936  df-dif 3856  df-nul 4222

This theorem is referenced by: (None)