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 e. CC -> ( A + 1 ) e. CC )

Proof of Theorem peano2cn

Step	Hyp	Ref	Expression
1		ax-1cn 8236	. 2 |- 1 e. CC
2		addcl 8268	. 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 2205  (class class class)co 6058   CCcc 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  15837  lgseisenlem1  16069  lgsquadlem1  16076