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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 12602 | . 2 ⊢ ℕ0 ⊆ ℕ0* | |
| 2 | 1 | sseli 3979 | 1 ⊢ (𝐴 ∈ ℕ0 → 𝐴 ∈ ℕ0*) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∈ wcel 2108 ℕ0cn0 12526 ℕ0*cxnn0 12599 | 
| 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-8 2110 ax-9 2118 ax-ext 2708 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-un 3956 df-ss 3968 df-xnn0 12600 | 
| This theorem is referenced by: xnn0xadd0 13289 wlk1ewlk 29658 frgrregorufrg 30345 usgrcyclgt2v 35136 | 
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