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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-n0i | Structured version Visualization version GIF version |
Description: Inference associated with n0 4339. Shortens 2ndcdisj 23284 (2888>2878), notzfaus 5352 (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 4339 | . 2 ⊢ (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴) | |
3 | 1, 2 | mpbi 229 | 1 ⊢ ∃𝑥 𝑥 ∈ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∃wex 1773 ∈ wcel 2098 ≠ wne 2932 ∅c0 4315 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-9 2108 ax-ext 2695 |
This theorem depends on definitions: df-bi 206 df-an 396 df-tru 1536 df-fal 1546 df-ex 1774 df-sb 2060 df-clab 2702 df-cleq 2716 df-ne 2933 df-dif 3944 df-nul 4316 |
This theorem is referenced by: (None) |
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