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| Mirrors > Home > MPE Home > Th. List > Mathboxes > unt0 | Structured version Visualization version GIF version | ||
| Description: The null set is untangled. (Contributed by Scott Fenton, 10-Mar-2011.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) | 
| Ref | Expression | 
|---|---|
| unt0 | ⊢ ∀𝑥 ∈ ∅ ¬ 𝑥 ∈ 𝑥 | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | ral0 4513 | 1 ⊢ ∀𝑥 ∈ ∅ ¬ 𝑥 ∈ 𝑥 | 
| Colors of variables: wff setvar class | 
| Syntax hints: ¬ wn 3 ∀wral 3061 ∅c0 4333 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-9 2118 ax-ext 2708 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-fal 1553 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-ral 3062 df-dif 3954 df-nul 4334 | 
| This theorem is referenced by: (None) | 
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