Theorem rpret 6222

Description: A positive real is a real.

Assertion

Ref	Expression
rpret	|- (A e. RR+ -> A e. RR)

Proof of Theorem rpret

Step	Hyp	Ref	Expression
1		df-rp 6219	. . 3 |- RR+ = {x e. RR | 0 < x}
2		ssrab2 2121	. . 3 |- {x e. RR | 0 < x} (_ RR
3	1, 2	eqsstr 2081	. 2 |- RR+ (_ RR
4	3	sseli 2055	1 |- (A e. RR+ -> A e. RR)

Syntax hints:   -> wi 3   e. wcel 955  {crab 1640   class class class wbr 2609  RRcr 5205  0cc0 5206  RR+crp 5272   < clt 5458

This theorem is referenced by:  rpssre 6223  rpge0t 6225  rpaddclt 6227  rpmulclt 6228  rpdivclt 6229  rpsqrclt 6645  abscncflem 7209  ivthlem6 7221  ivthlem7 7222  ivthlem6OLD 7230  ivthlem7OLD 7231  minveclem24 8499  minveclem25 8500  minveclem26 8501  minveclem27 8502  minveclem28 8503  pire 8596  reeflogt 8683  relogeftb 8687  mslb1 10473  2wsms 10474  iintlem1 10476  iint 10478

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-rab 1644  df-in 2041  df-ss 2043  df-rp 6219

Copyright terms: Public domain