Theorem peano2cn 8242

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4661. (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 8053	. 2 |- 1 e. CC
2		addcl 8085	. 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 2178  (class class class)co 5967   CCcc 7958   1c1 7961   + caddc 7963

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8053  ax-addcl 8056

This theorem is referenced by:  xp1d2m1eqxm1d2  9325  nneo  9511  zeo  9513  zeo2  9514  zesq  10840  facndiv  10921  faclbnd  10923  faclbnd6  10926  bcxmas  11915  trireciplem  11926  odd2np1  12299  abssinper  15433  lgseisenlem1  15662  lgsquadlem1  15669