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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-n0i | Structured version Visualization version GIF version |
Description: Inference associated with n0 4307. Shortens 2ndcdisj 21992 (2888>2878), notzfaus 5253 (264>253). (Contributed by BJ, 22-Apr-2019.) |
Ref | Expression |
---|---|
bj-n0i.1 | ⊢ 𝐴 ≠ ∅ |
Ref | Expression |
---|---|
bj-n0i | ⊢ ∃𝑥 𝑥 ∈ 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-n0i.1 | . 2 ⊢ 𝐴 ≠ ∅ | |
2 | n0 4307 | . 2 ⊢ (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴) | |
3 | 1, 2 | mpbi 231 | 1 ⊢ ∃𝑥 𝑥 ∈ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∃wex 1771 ∈ wcel 2105 ≠ wne 3013 ∅c0 4288 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-11 2151 ax-12 2167 ax-ext 2790 |
This theorem depends on definitions: df-bi 208 df-an 397 df-or 842 df-tru 1531 df-ex 1772 df-nf 1776 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 df-nfc 2960 df-ne 3014 df-dif 3936 df-nul 4289 |
This theorem is referenced by: (None) |
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