Theorem peano2cn 8304

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4691. (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 8115	. 2 |- 1 e. CC
2		addcl 8147	. 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 6013   CCcc 8020   1c1 8023   + caddc 8025

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8115  ax-addcl 8118

This theorem is referenced by:  xp1d2m1eqxm1d2  9387  nneo  9573  zeo  9575  zeo2  9576  zesq  10910  facndiv  10991  faclbnd  10993  faclbnd6  10996  bcxmas  12040  trireciplem  12051  odd2np1  12424  abssinper  15560  lgseisenlem1  15789  lgsquadlem1  15796