Theorem peano2cn 8424

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4722. (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 8236	. 2 ⊢ 1 ∈ ℂ
2		addcl 8268	. 2 ⊢ ((𝐴 ∈ ℂ ∧ 1 ∈ ℂ) → (𝐴 + 1) ∈ ℂ)
3	1, 2	mpan2 425	1 ⊢ (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ)

Syntax hints:   → wi 4   ∈ wcel 2205  (class class class)co 6058  ℂcc 8141  1c1 8144   + caddc 8146

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8236  ax-addcl 8239

This theorem is referenced by:  xp1d2m1eqxm1d2  9508  nneo  9699  zeo  9701  zeo2  9702  zesq  11045  facndiv  11126  faclbnd  11128  faclbnd6  11131  bcxmas  12200  trireciplem  12211  odd2np1  12584  abssinper  15823  lgseisenlem1  16055  lgsquadlem1  16062