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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-n0i | Structured version Visualization version GIF version |
Description: Inference associated with n0 3890. (Minimizes three statements by a total of 29 bytes.) (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 3890 | . 2 ⊢ (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴) | |
3 | 1, 2 | mpbi 219 | 1 ⊢ ∃𝑥 𝑥 ∈ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∃wex 1695 ∈ wcel 1977 ≠ wne 2780 ∅c0 3874 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-ne 2782 df-v 3175 df-dif 3543 df-nul 3875 |
This theorem is referenced by: (None) |
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