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Theorem rpssre 9693
Description: The positive reals are a subset of the reals. (Contributed by NM, 24-Feb-2008.)
Assertion
Ref Expression
rpssre + ⊆ ℝ

Proof of Theorem rpssre
StepHypRef Expression
1 rpre 9689 . 2 (𝑥 ∈ ℝ+𝑥 ∈ ℝ)
21ssriv 3174 1 + ⊆ ℝ
Colors of variables: wff set class
Syntax hints:  wss 3144  cr 7839  +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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