Theorem rpssre 9898

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 9894	. 2 ⊢ (𝑥 ∈ ℝ+ → 𝑥 ∈ ℝ)
2	1	ssriv 3231	1 ⊢ ℝ+ ⊆ ℝ

Syntax hints:   ⊆ wss 3200  ℝcr 8030  ℝ⁺crp 9887

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-rab 2519  df-in 3206  df-ss 3213  df-rp 9888

This theorem is referenced by:  rpred  9930  rpexpcl  10819  resqrexlemcvg  11579  resqrexlemsqa  11584  fsumrpcl  11964  fprodrpcl  12171  metuex  14568