Theorem rpssre 9997

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 9993	. 2 |- ( x e. RR+ -> x e. RR )
2	1	ssriv 3242	1 |- RR+ C_ RR

Syntax hints:   C_ wss 3211   RRcr 8126   RR+crp 9986

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-rab 2529  df-in 3217  df-ss 3224  df-rp 9987

This theorem is referenced by:  rpred  10029  rpexpcl  10920  resqrexlemcvg  11704  resqrexlemsqa  11709  fsumrpcl  12090  fprodrpcl  12297  metuex  14703