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Mirrors > Home > ILE Home > Th. List > rpssre | GIF version |
Description: The positive reals are a subset of the reals. (Contributed by NM, 24-Feb-2008.) |
Ref | Expression |
---|---|
rpssre | ⊢ ℝ+ ⊆ ℝ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpre 9689 | . 2 ⊢ (𝑥 ∈ ℝ+ → 𝑥 ∈ ℝ) | |
2 | 1 | ssriv 3174 | 1 ⊢ ℝ+ ⊆ ℝ |
Colors of variables: wff set class |
Syntax hints: ⊆ wss 3144 ℝcr 7839 ℝ+crp 9682 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rab 2477 df-in 3150 df-ss 3157 df-rp 9683 |
This theorem is referenced by: rpred 9725 rpexpcl 10569 resqrexlemcvg 11059 resqrexlemsqa 11064 fsumrpcl 11443 fprodrpcl 11650 |
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