Theorem peano2cn 8207

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4643. (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 8018	. 2 |- 1 e. CC
2		addcl 8050	. 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 2176  (class class class)co 5944   CCcc 7923   1c1 7926   + caddc 7928

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8018  ax-addcl 8021

This theorem is referenced by:  xp1d2m1eqxm1d2  9290  nneo  9476  zeo  9478  zeo2  9479  zesq  10803  facndiv  10884  faclbnd  10886  faclbnd6  10889  bcxmas  11800  trireciplem  11811  odd2np1  12184  abssinper  15318  lgseisenlem1  15547  lgsquadlem1  15554