Theorem peano2cn 8451

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4737. (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 8262	. 2 |- 1 e. CC
2		addcl 8294	. 2 |- ( ( A e. CC /\ 1 e. CC ) -> ( A + 1 ) e. CC )
3	1, 2	mpan2 429	1 |- ( A e. CC -> ( A + 1 ) e. CC )

Syntax hints:   -> wi 4   e. wcel 2209  (class class class)co 6075   CCcc 8167   1c1 8170   + caddc 8172

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8262  ax-addcl 8265

This theorem is referenced by:  xp1d2m1eqxm1d2  9537  nneo  9728  zeo  9730  zeo2  9731  zesq  11074  facndiv  11155  faclbnd  11157  faclbnd6  11160  bcxmas  12234  trireciplem  12245  odd2np1  12618  abssinper  15870  lgseisenlem1  16103  lgsquadlem1  16110