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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-1nel0 | Structured version Visualization version GIF version |
Description: 1𝑜 does not belong to {∅}. (Contributed by BJ, 6-Apr-2019.) |
Ref | Expression |
---|---|
bj-1nel0 | ⊢ 1𝑜 ∉ {∅} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1n0 7620 | . . . 4 ⊢ 1𝑜 ≠ ∅ | |
2 | 1 | neii 2825 | . . 3 ⊢ ¬ 1𝑜 = ∅ |
3 | elsni 4227 | . . 3 ⊢ (1𝑜 ∈ {∅} → 1𝑜 = ∅) | |
4 | 2, 3 | mto 188 | . 2 ⊢ ¬ 1𝑜 ∈ {∅} |
5 | 4 | nelir 2929 | 1 ⊢ 1𝑜 ∉ {∅} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1523 ∈ wcel 2030 ∉ wnel 2926 ∅c0 3948 {csn 4210 1𝑜c1o 7598 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1762 ax-4 1777 ax-5 1879 ax-6 1945 ax-7 1981 ax-9 2039 ax-10 2059 ax-11 2074 ax-12 2087 ax-13 2282 ax-ext 2631 ax-nul 4822 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-tru 1526 df-ex 1745 df-nf 1750 df-sb 1938 df-clab 2638 df-cleq 2644 df-clel 2647 df-nfc 2782 df-ne 2824 df-nel 2927 df-v 3233 df-dif 3610 df-un 3612 df-nul 3949 df-sn 4211 df-suc 5767 df-1o 7605 |
This theorem is referenced by: (None) |
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