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Theorem rpssre 9445
 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 9441 . 2 (𝑥 ∈ ℝ+𝑥 ∈ ℝ)
21ssriv 3096 1 + ⊆ ℝ
 Colors of variables: wff set class Syntax hints:   ⊆ wss 3066  ℝcr 7612  ℝ+crp 9434 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rab 2423  df-in 3072  df-ss 3079  df-rp 9435 This theorem is referenced by:  rpred  9476  rpexpcl  10305  resqrexlemcvg  10784  resqrexlemsqa  10789  fsumrpcl  11166
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