Theorem rpssre 9788

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 9784	. 2 |- ( x e. RR+ -> x e. RR )
2	1	ssriv 3197	1 |- RR+ C_ RR

Syntax hints:   C_ wss 3166   RRcr 7926   RR+crp 9777

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-rab 2493  df-in 3172  df-ss 3179  df-rp 9778

This theorem is referenced by:  rpred  9820  rpexpcl  10705  resqrexlemcvg  11363  resqrexlemsqa  11368  fsumrpcl  11748  fprodrpcl  11955  metuex  14350