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Theorem rrpsscn 27719
Description: The positive reals are a subset of the complex numbers. (Contributed by Glauco Siliprandi, 29-Jun-2017.)
Assertion
Ref Expression
rrpsscn  |-  RR+  C_  CC

Proof of Theorem rrpsscn
StepHypRef Expression
1 rpcn 10362 . . 3  |-  ( x  e.  RR+  ->  x  e.  CC )
21ax-gen 1533 . 2  |-  A. x
( x  e.  RR+  ->  x  e.  CC )
3 dfss2 3169 . 2  |-  ( RR+  C_  CC  <->  A. x ( x  e.  RR+  ->  x  e.  CC ) )
42, 3mpbir 200 1  |-  RR+  C_  CC
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527    e. wcel 1684    C_ wss 3152   CCcc 8735   RR+crp 10354
This theorem is referenced by:  stirlinglem8  27830
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-resscn 8794
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rab 2552  df-in 3159  df-ss 3166  df-rp 10355
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