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Mirrors > Home > MPE Home > Th. List > nnssnn0 | Structured version Visualization version Unicode version |
Description: Positive naturals are a subset of nonnegative integers. (Contributed by Raph Levien, 10-Dec-2002.) |
Ref | Expression |
---|---|
nnssnn0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssun1 3776 | . 2 | |
2 | df-n0 11293 | . 2 | |
3 | 1, 2 | sseqtr4i 3638 | 1 |
Colors of variables: wff setvar class |
Syntax hints: cun 3572 wss 3574 csn 4177 cc0 9936 cn 11020 cn0 11292 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-un 3579 df-in 3581 df-ss 3588 df-n0 11293 |
This theorem is referenced by: nnnn0 11299 nnnn0d 11351 nthruz 14982 oddge22np1 15073 bitsfzolem 15156 lcmfval 15334 ramub1 15732 ramcl 15733 ply1divex 23896 pserdvlem2 24182 fsum2dsub 30685 breprexplemc 30710 breprexpnat 30712 knoppndvlem18 32520 hbtlem5 37698 brfvtrcld 38013 corcltrcl 38031 fourierdlem50 40373 fourierdlem102 40425 fourierdlem114 40437 fmtnoinf 41448 fmtnofac2 41481 |
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