Theorem peano2cn 8455

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4740. (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 8266	. 2 ⊢ 1 ∈ ℂ
2		addcl 8298	. 2 ⊢ ((𝐴 ∈ ℂ ∧ 1 ∈ ℂ) → (𝐴 + 1) ∈ ℂ)
3	1, 2	mpan2 429	1 ⊢ (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ)

Syntax hints:   → wi 4   ∈ wcel 2209  (class class class)co 6079  ℂcc 8171  1c1 8174   + caddc 8176

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8266  ax-addcl 8269

This theorem is referenced by:  xp1d2m1eqxm1d2  9541  nneo  9732  zeo  9734  zeo2  9735  zesq  11079  facndiv  11160  faclbnd  11162  faclbnd6  11165  bcxmas  12239  trireciplem  12250  odd2np1  12623  abssinper  15930  lgseisenlem1  16172  lgsquadlem1  16179