Theorem peano2cn 8277

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4686. (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 8088	. 2 |- 1 e. CC
2		addcl 8120	. 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 6000   CCcc 7993   1c1 7996   + caddc 7998

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8088  ax-addcl 8091

This theorem is referenced by:  xp1d2m1eqxm1d2  9360  nneo  9546  zeo  9548  zeo2  9549  zesq  10875  facndiv  10956  faclbnd  10958  faclbnd6  10961  bcxmas  11995  trireciplem  12006  odd2np1  12379  abssinper  15514  lgseisenlem1  15743  lgsquadlem1  15750