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

Theorem peano2cn 7299
Description: A theorem for complex numbers analogous the second Peano postulate peano2 4338. (Contributed by NM, 17-Aug-2005.)
Assertion
Ref Expression
peano2cn (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ)

Proof of Theorem peano2cn
StepHypRef Expression
1 ax-1cn 7120 . 2 1 ∈ ℂ
2 addcl 7149 . 2 ((𝐴 ∈ ℂ ∧ 1 ∈ ℂ) → (𝐴 + 1) ∈ ℂ)
31, 2mpan2 416 1 (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1434  (class class class)co 5537  cc 7030  1c1 7033   + caddc 7035
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106  ax-1cn 7120  ax-addcl 7123
This theorem is referenced by:  xp1d2m1eqxm1d2  8339  nneo  8520  zeo  8522  zeo2  8523  zesq  9677  facndiv  9752  faclbnd  9754  faclbnd6  9757  odd2np1  10406
  Copyright terms: Public domain W3C validator