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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 8589 | . 2 ⊢ (𝑥 ∈ ℝ+ → 𝑥 ∈ ℝ) | |
2 | 1 | ssriv 2949 | 1 ⊢ ℝ+ ⊆ ℝ |
Colors of variables: wff set class |
Syntax hints: ⊆ wss 2917 ℝcr 6888 ℝ+crp 8583 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rab 2315 df-in 2924 df-ss 2931 df-rp 8584 |
This theorem is referenced by: rpred 8622 rpexpcl 9274 resqrexlemf 9605 resqrexlemf1 9606 resqrexlemfp1 9607 resqrexlemcvg 9617 resqrexlemsqa 9622 |
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