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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 4455 | 1 ⊢ ∀𝑥 ∈ ∅ ¬ 𝑥 ∈ 𝑥 |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∀wral 3138 ∅c0 4290 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1777 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-ral 3143 df-dif 3938 df-nul 4291 |
This theorem is referenced by: (None) |
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