ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  peano2cn Unicode version

Theorem peano2cn 7380
Description: A theorem for complex numbers analogous the second Peano postulate peano2 4364. (Contributed by NM, 17-Aug-2005.)
Assertion
Ref Expression
peano2cn  |-  ( A  e.  CC  ->  ( A  +  1 )  e.  CC )

Proof of Theorem peano2cn
StepHypRef Expression
1 ax-1cn 7201 . 2  |-  1  e.  CC
2 addcl 7230 . 2  |-  ( ( A  e.  CC  /\  1  e.  CC )  ->  ( A  +  1 )  e.  CC )
31, 2mpan2 416 1  |-  ( A  e.  CC  ->  ( A  +  1 )  e.  CC )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1434  (class class class)co 5564   CCcc 7111   1c1 7114    + caddc 7116
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106  ax-1cn 7201  ax-addcl 7204
This theorem is referenced by:  xp1d2m1eqxm1d2  8420  nneo  8601  zeo  8603  zeo2  8604  zesq  9758  facndiv  9833  faclbnd  9835  faclbnd6  9838  odd2np1  10498
  Copyright terms: Public domain W3C validator