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Theorem peano2cn 7596
Description: A theorem for complex numbers analogous the second Peano postulate peano2 4400. (Contributed by NM, 17-Aug-2005.)
Assertion
Ref Expression
peano2cn (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ)

Proof of Theorem peano2cn
StepHypRef Expression
1 ax-1cn 7417 . 2 1 ∈ ℂ
2 addcl 7446 . 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 1438  (class class class)co 5634  cc 7327  1c1 7330   + caddc 7332
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106  ax-1cn 7417  ax-addcl 7420
This theorem is referenced by:  xp1d2m1eqxm1d2  8638  nneo  8819  zeo  8821  zeo2  8822  zesq  10037  facndiv  10112  faclbnd  10114  faclbnd6  10117  bcxmas  10845  trireciplem  10855  odd2np1  10966
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