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Theorem peano2cn 8054
Description: A theorem for complex numbers analogous the second Peano postulate peano2 4579. (Contributed by NM, 17-Aug-2005.)
Assertion
Ref Expression
peano2cn (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ)

Proof of Theorem peano2cn
StepHypRef Expression
1 ax-1cn 7867 . 2 1 ∈ ℂ
2 addcl 7899 . 2 ((𝐴 ∈ ℂ ∧ 1 ∈ ℂ) → (𝐴 + 1) ∈ ℂ)
31, 2mpan2 423 1 (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 2141  (class class class)co 5853  cc 7772  1c1 7775   + caddc 7777
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-1cn 7867  ax-addcl 7870
This theorem is referenced by:  xp1d2m1eqxm1d2  9130  nneo  9315  zeo  9317  zeo2  9318  zesq  10594  facndiv  10673  faclbnd  10675  faclbnd6  10678  bcxmas  11452  trireciplem  11463  odd2np1  11832  abssinper  13561
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