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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-n0i | Structured version Visualization version GIF version |
Description: Inference associated with n0 3931. Shortens 2ndcdisj 21259 (2888>2878), notzfaus 4840 (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 3931 | . 2 ⊢ (𝐴 ≠ ∅ ↔ ∃𝑥 𝑥 ∈ 𝐴) | |
3 | 1, 2 | mpbi 220 | 1 ⊢ ∃𝑥 𝑥 ∈ 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: ∃wex 1704 ∈ wcel 1990 ≠ wne 2794 ∅c0 3915 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-v 3202 df-dif 3577 df-nul 3916 |
This theorem is referenced by: (None) |
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