Theorem peano2cn 8408

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4717. (Contributed by NM, 17-Aug-2005.)

Assertion

Ref	Expression
peano2cn	|- ( A e. CC -> ( A + 1 ) e. CC )

Proof of Theorem peano2cn

Step	Hyp	Ref	Expression
1		ax-1cn 8220	. 2 |- 1 e. CC
2		addcl 8252	. 2 |- ( ( A e. CC /\ 1 e. CC ) -> ( A + 1 ) e. CC )
3	1, 2	mpan2 425	1 |- ( A e. CC -> ( A + 1 ) e. CC )

Syntax hints:   -> wi 4   e. wcel 2203  (class class class)co 6050   CCcc 8125   1c1 8128   + caddc 8130

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8220  ax-addcl 8223

This theorem is referenced by:  xp1d2m1eqxm1d2  9491  nneo  9681  zeo  9683  zeo2  9684  zesq  11020  facndiv  11101  faclbnd  11103  faclbnd6  11106  bcxmas  12175  trireciplem  12186  odd2np1  12559  abssinper  15711  lgseisenlem1  15943  lgsquadlem1  15950