Theorem peano2cn 8086

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4592. (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 7899	. 2 |- 1 e. CC
2		addcl 7931	. 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 2148  (class class class)co 5870   CCcc 7804   1c1 7807   + caddc 7809

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 7899  ax-addcl 7902

This theorem is referenced by:  xp1d2m1eqxm1d2  9165  nneo  9350  zeo  9352  zeo2  9353  zesq  10631  facndiv  10710  faclbnd  10712  faclbnd6  10715  bcxmas  11488  trireciplem  11499  odd2np1  11868  abssinper  14049