Theorem peano2cn 7299

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4338. (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 7120	. 2 ⊢ 1 ∈ ℂ
2		addcl 7149	. 2 ⊢ ((𝐴 ∈ ℂ ∧ 1 ∈ ℂ) → (𝐴 + 1) ∈ ℂ)
3	1, 2	mpan2 416	1 ⊢ (𝐴 ∈ ℂ → (𝐴 + 1) ∈ ℂ)

Syntax hints:   → wi 4   ∈ wcel 1434  (class class class)co 5537  ℂcc 7030  1c1 7033   + caddc 7035

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106  ax-1cn 7120  ax-addcl 7123

This theorem is referenced by:  xp1d2m1eqxm1d2  8339  nneo  8520  zeo  8522  zeo2  8523  zesq  9677  facndiv  9752  faclbnd  9754  faclbnd6  9757  odd2np1  10406