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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 9140 | . 2 ⊢ (𝑥 ∈ ℝ+ → 𝑥 ∈ ℝ) | |
2 | 1 | ssriv 3029 | 1 ⊢ ℝ+ ⊆ ℝ |
Colors of variables: wff set class |
Syntax hints: ⊆ wss 2999 ℝcr 7349 ℝ+crp 9134 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-rab 2368 df-in 3005 df-ss 3012 df-rp 9135 |
This theorem is referenced by: rpred 9173 rpexpcl 9974 resqrexlemcvg 10452 resqrexlemsqa 10457 fsumrpcl 10798 |
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