Theorem rpssre 9730

Description: The positive reals are a subset of the reals. (Contributed by NM, 24-Feb-2008.)

Assertion

Ref	Expression
rpssre	⊢ ℝ+ ⊆ ℝ

Proof of Theorem rpssre

Step	Hyp	Ref	Expression
1		rpre 9726	. 2 ⊢ (𝑥 ∈ ℝ+ → 𝑥 ∈ ℝ)
2	1	ssriv 3183	1 ⊢ ℝ+ ⊆ ℝ

Syntax hints:   ⊆ wss 3153  ℝcr 7871  ℝ⁺crp 9719

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 2175

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-rab 2481  df-in 3159  df-ss 3166  df-rp 9720

This theorem is referenced by:  rpred  9762  rpexpcl  10629  resqrexlemcvg  11163  resqrexlemsqa  11168  fsumrpcl  11547  fprodrpcl  11754