Theorem bj-n0i 36946

Description: Inference associated with n0 4360. Shortens 2ndcdisj 23486 (2888>2878), notzfaus 5370 (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 4360	. 2 ⊢ (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴)
3	1, 2	mpbi 230	1 ⊢ ∃𝑥 𝑥 ∈ 𝐴

Syntax hints:  ∃wex 1777   ∈ wcel 2107   ≠ wne 2939  ∅c0 4340

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1966  ax-7 2006  ax-9 2117  ax-ext 2707

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1541  df-fal 1551  df-ex 1778  df-sb 2064  df-clab 2714  df-cleq 2728  df-ne 2940  df-dif 3967  df-nul 4341

This theorem is referenced by: (None)