Theorem peano2cn 8314

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4693. (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 8125	. 2 |- 1 e. CC
2		addcl 8157	. 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 2202  (class class class)co 6018   CCcc 8030   1c1 8033   + caddc 8035

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8125  ax-addcl 8128

This theorem is referenced by:  xp1d2m1eqxm1d2  9397  nneo  9583  zeo  9585  zeo2  9586  zesq  10921  facndiv  11002  faclbnd  11004  faclbnd6  11007  bcxmas  12068  trireciplem  12079  odd2np1  12452  abssinper  15589  lgseisenlem1  15818  lgsquadlem1  15825