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Theorem peano2cn 7919
Description: A theorem for complex numbers analogous the second Peano postulate peano2 4515. (Contributed by NM, 17-Aug-2005.)
Assertion
Ref Expression
peano2cn (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ)

Proof of Theorem peano2cn
StepHypRef Expression
1 ax-1cn 7735 . 2 1 ∈ ℂ
2 addcl 7767 . 2 ((𝐴 ∈ ℂ ∧ 1 ∈ ℂ) → (𝐴 + 1) ∈ ℂ)
31, 2mpan2 422 1 (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1481  (class class class)co 5780  cc 7640  1c1 7643   + caddc 7645
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-1cn 7735  ax-addcl 7738
This theorem is referenced by:  xp1d2m1eqxm1d2  8994  nneo  9176  zeo  9178  zeo2  9179  zesq  10439  facndiv  10515  faclbnd  10517  faclbnd6  10520  bcxmas  11288  trireciplem  11299  odd2np1  11599  abssinper  12968
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