Theorem rpssre 9600

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

Assertion

Ref	Expression
rpssre	|- RR+ C_ RR

Proof of Theorem rpssre

Step	Hyp	Ref	Expression
1		rpre 9596	. 2 |- ( x e. RR+ -> x e. RR )
2	1	ssriv 3146	1 |- RR+ C_ RR

Syntax hints:   C_ wss 3116   RRcr 7752   RR+crp 9589

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 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-rab 2453  df-in 3122  df-ss 3129  df-rp 9590

This theorem is referenced by:  rpred  9632  rpexpcl  10474  resqrexlemcvg  10961  resqrexlemsqa  10966  fsumrpcl  11345  fprodrpcl  11552