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Mirrors > Home > MPE Home > Th. List > 0xnn0 | Structured version Visualization version GIF version |
Description: Zero is an extended nonnegative integer. (Contributed by AV, 10-Dec-2020.) |
Ref | Expression |
---|---|
0xnn0 | ⊢ 0 ∈ ℕ0* |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nn0ssxnn0 11776 | . 2 ⊢ ℕ0 ⊆ ℕ0* | |
2 | 0nn0 11718 | . 2 ⊢ 0 ∈ ℕ0 | |
3 | 1, 2 | sselii 3849 | 1 ⊢ 0 ∈ ℕ0* |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2050 0cc0 10329 ℕ0cn0 11701 ℕ0*cxnn0 11773 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1758 ax-4 1772 ax-5 1869 ax-6 1928 ax-7 1965 ax-8 2052 ax-9 2059 ax-10 2079 ax-11 2093 ax-12 2106 ax-ext 2744 ax-1cn 10387 ax-icn 10388 ax-addcl 10389 ax-mulcl 10391 ax-i2m1 10397 |
This theorem depends on definitions: df-bi 199 df-an 388 df-or 834 df-tru 1510 df-ex 1743 df-nf 1747 df-sb 2016 df-clab 2753 df-cleq 2765 df-clel 2840 df-nfc 2912 df-v 3411 df-un 3828 df-in 3830 df-ss 3837 df-sn 4436 df-n0 11702 df-xnn0 11774 |
This theorem is referenced by: 0edg0rgr 27051 rgrusgrprc 27068 rusgrprc 27069 rgrprcx 27071 |
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