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Theorem rpssre 8691
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 8687 . 2 (𝑥 ∈ ℝ+𝑥 ∈ ℝ)
21ssriv 2977 1 + ⊆ ℝ
Colors of variables: wff set class
Syntax hints:  wss 2945  cr 6946  +crp 8681
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rab 2332  df-in 2952  df-ss 2959  df-rp 8682
This theorem is referenced by:  rpred  8720  rpexpcl  9439  resqrexlemf  9834  resqrexlemf1  9835  resqrexlemfp1  9836  resqrexlemcvg  9846  resqrexlemsqa  9851
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