Theorem peano2cn 8024

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4566. (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 7837	. 2 ⊢ 1 ∈ ℂ
2		addcl 7869	. 2 ⊢ ((𝐴 ∈ ℂ ∧ 1 ∈ ℂ) → (𝐴 + 1) ∈ ℂ)
3	1, 2	mpan2 422	1 ⊢ (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ)

Syntax hints:   → wi 4   ∈ wcel 2135  (class class class)co 5836  ℂcc 7742  1c1 7745   + caddc 7747

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-1cn 7837  ax-addcl 7840

This theorem is referenced by:  xp1d2m1eqxm1d2  9100  nneo  9285  zeo  9287  zeo2  9288  zesq  10562  facndiv  10641  faclbnd  10643  faclbnd6  10646  bcxmas  11416  trireciplem  11427  odd2np1  11795  abssinper  13308