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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 8307 | . . . 4 ⊢ 1o ≠ ∅ | |
2 | 1 | neii 2945 | . . 3 ⊢ ¬ 1o = ∅ |
3 | elsni 4580 | . . 3 ⊢ (1o ∈ {∅} → 1o = ∅) | |
4 | 2, 3 | mto 196 | . 2 ⊢ ¬ 1o ∈ {∅} |
5 | 4 | nelir 3052 | 1 ⊢ 1o ∉ {∅} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1539 ∈ wcel 2106 ∉ wnel 3049 ∅c0 4258 {csn 4563 1oc1o 8279 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2709 ax-nul 5230 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-tru 1542 df-fal 1552 df-ex 1783 df-sb 2068 df-clab 2716 df-cleq 2730 df-clel 2816 df-ne 2944 df-nel 3050 df-v 3433 df-dif 3891 df-un 3893 df-nul 4259 df-sn 4564 df-suc 6267 df-1o 8286 |
This theorem is referenced by: (None) |
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