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Mirrors > Home > MPE Home > Th. List > nn0xnn0 | Structured version Visualization version GIF version |
Description: A standard nonnegative integer is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.) |
Ref | Expression |
---|---|
nn0xnn0 | ⊢ (𝐴 ∈ ℕ0 → 𝐴 ∈ ℕ0*) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0ssxnn0 11243 | . 2 ⊢ ℕ0 ⊆ ℕ0* | |
2 | 1 | sseli 3564 | 1 ⊢ (𝐴 ∈ ℕ0 → 𝐴 ∈ ℕ0*) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 1977 ℕ0cn0 11169 ℕ0*cxnn0 11240 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-v 3175 df-un 3545 df-in 3547 df-ss 3554 df-xnn0 11241 |
This theorem is referenced by: xnn0xadd0 11949 1wlk1ewlk 40844 frgrregorufrg 41505 |
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