Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > nn0ssre | Unicode version |
Description: Nonnegative integers are a subset of the reals. (Contributed by Raph Levien, 10-Dec-2002.) |
Ref | Expression |
---|---|
nn0ssre |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-n0 9136 | . 2 | |
2 | nnssre 8882 | . . 3 | |
3 | 0re 7920 | . . . 4 | |
4 | snssi 3724 | . . . 4 | |
5 | 3, 4 | ax-mp 5 | . . 3 |
6 | 2, 5 | unssi 3302 | . 2 |
7 | 1, 6 | eqsstri 3179 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 2141 cun 3119 wss 3121 csn 3583 cr 7773 cc0 7774 cn 8878 cn0 9135 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 ax-sep 4107 ax-cnex 7865 ax-resscn 7866 ax-1re 7868 ax-addrcl 7871 ax-rnegex 7883 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-sn 3589 df-int 3832 df-inn 8879 df-n0 9136 |
This theorem is referenced by: nn0sscn 9140 nn0re 9144 nn0rei 9146 nn0red 9189 |
Copyright terms: Public domain | W3C validator |