Theorem rpssre 10065

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 10061	. 2 |- ( x e. RR+ -> x e. RR )
2	1	ssriv 3252	1 |- RR+ C_ RR

This proof depends on syntax axioms:   C_ wss 3220   RRcr 8178   RR+crp 10054

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-rab 2537  df-in 3226  df-ss 3233  df-rp 10055

This theorem is used by:  rpred  10097  rpexpcl  10995  resqrexlemcvg  11785  resqrexlemsqa  11790  fsumrpcl  12171  fprodrpcl  12378  metuex  14892