Theorem peano2cn 8220

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4648. (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 8031	. 2 ⊢ 1 ∈ ℂ
2		addcl 8063	. 2 ⊢ ((𝐴 ∈ ℂ ∧ 1 ∈ ℂ) → (𝐴 + 1) ∈ ℂ)
3	1, 2	mpan2 425	1 ⊢ (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ)

Syntax hints:   → wi 4   ∈ wcel 2177  (class class class)co 5954  ℂcc 7936  1c1 7939   + caddc 7941

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8031  ax-addcl 8034

This theorem is referenced by:  xp1d2m1eqxm1d2  9303  nneo  9489  zeo  9491  zeo2  9492  zesq  10816  facndiv  10897  faclbnd  10899  faclbnd6  10902  bcxmas  11850  trireciplem  11861  odd2np1  12234  abssinper  15368  lgseisenlem1  15597  lgsquadlem1  15604