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Theorem rpssre 9144
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 9140 . 2 (𝑥 ∈ ℝ+𝑥 ∈ ℝ)
21ssriv 3029 1 + ⊆ ℝ
Colors of variables: wff set class
Syntax hints:  wss 2999  cr 7349  +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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