Theorem peano2cn 8314

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4693. (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 8125	. 2 ⊢ 1 ∈ ℂ
2		addcl 8157	. 2 ⊢ ((𝐴 ∈ ℂ ∧ 1 ∈ ℂ) → (𝐴 + 1) ∈ ℂ)
3	1, 2	mpan2 425	1 ⊢ (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ)

Syntax hints:   → wi 4   ∈ wcel 2202  (class class class)co 6018  ℂcc 8030  1c1 8033   + caddc 8035

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8125  ax-addcl 8128

This theorem is referenced by:  xp1d2m1eqxm1d2  9397  nneo  9583  zeo  9585  zeo2  9586  zesq  10921  facndiv  11002  faclbnd  11004  faclbnd6  11007  bcxmas  12055  trireciplem  12066  odd2np1  12439  abssinper  15576  lgseisenlem1  15805  lgsquadlem1  15812