Theorem peano2cn 7897

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4509. (Contributed by NM, 17-Aug-2005.)

Assertion

Ref	Expression
peano2cn	⊢ (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ)

Proof of Theorem peano2cn

Step	Hyp	Ref	Expression
1		ax-1cn 7713	. 2 ⊢ 1 ∈ ℂ
2		addcl 7745	. 2 ⊢ ((𝐴 ∈ ℂ ∧ 1 ∈ ℂ) → (𝐴 + 1) ∈ ℂ)
3	1, 2	mpan2 421	1 ⊢ (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ)

Syntax hints:   → wi 4   ∈ wcel 1480  (class class class)co 5774  ℂcc 7618  1c1 7621   + caddc 7623

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-1cn 7713  ax-addcl 7716

This theorem is referenced by:  xp1d2m1eqxm1d2  8972  nneo  9154  zeo  9156  zeo2  9157  zesq  10410  facndiv  10485  faclbnd  10487  faclbnd6  10490  bcxmas  11258  trireciplem  11269  odd2np1  11570  abssinper  12927