Theorem peano2cn 8307

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4691. (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 8118	. 2 ⊢ 1 ∈ ℂ
2		addcl 8150	. 2 ⊢ ((𝐴 ∈ ℂ ∧ 1 ∈ ℂ) → (𝐴 + 1) ∈ ℂ)
3	1, 2	mpan2 425	1 ⊢ (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ)

Syntax hints:   → wi 4   ∈ wcel 2200  (class class class)co 6013  ℂcc 8023  1c1 8026   + caddc 8028

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8118  ax-addcl 8121

This theorem is referenced by:  xp1d2m1eqxm1d2  9390  nneo  9576  zeo  9578  zeo2  9579  zesq  10913  facndiv  10994  faclbnd  10996  faclbnd6  10999  bcxmas  12043  trireciplem  12054  odd2np1  12427  abssinper  15563  lgseisenlem1  15792  lgsquadlem1  15799