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Theorem rrpsscn 27822
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 10378 . . 3  |-  ( x  e.  RR+  ->  x  e.  CC )
21ax-gen 1536 . 2  |-  A. x
( x  e.  RR+  ->  x  e.  CC )
3 dfss2 3182 . 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 1530    e. wcel 1696    C_ wss 3165   CCcc 8751   RR+crp 10370
This theorem is referenced by:  stirlinglem8  27933
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-resscn 8810
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rab 2565  df-in 3172  df-ss 3179  df-rp 10371
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