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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-n0i | Structured version Visualization version GIF version |
Description: Inference associated with n0 4159. Shortens 2ndcdisj 21672 (2888>2878), notzfaus 5076 (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 4159 | . 2 ⊢ (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴) | |
3 | 1, 2 | mpbi 222 | 1 ⊢ ∃𝑥 𝑥 ∈ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∃wex 1823 ∈ wcel 2107 ≠ wne 2969 ∅c0 4141 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2055 ax-9 2116 ax-10 2135 ax-11 2150 ax-12 2163 ax-ext 2754 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 837 df-tru 1605 df-ex 1824 df-nf 1828 df-sb 2012 df-clab 2764 df-cleq 2770 df-clel 2774 df-nfc 2921 df-ne 2970 df-dif 3795 df-nul 4142 |
This theorem is referenced by: (None) |
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