Theorem peano2cn 8292

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4687. (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 8103	. 2 |- 1 e. CC
2		addcl 8135	. 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 2200  (class class class)co 6007   CCcc 8008   1c1 8011   + caddc 8013

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8103  ax-addcl 8106

This theorem is referenced by:  xp1d2m1eqxm1d2  9375  nneo  9561  zeo  9563  zeo2  9564  zesq  10892  facndiv  10973  faclbnd  10975  faclbnd6  10978  bcxmas  12016  trireciplem  12027  odd2np1  12400  abssinper  15536  lgseisenlem1  15765  lgsquadlem1  15772