Theorem peano2cn 8164

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4632. (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 7975	. 2 |- 1 e. CC
2		addcl 8007	. 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 2167  (class class class)co 5923   CCcc 7880   1c1 7883   + caddc 7885

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 7975  ax-addcl 7978

This theorem is referenced by:  xp1d2m1eqxm1d2  9247  nneo  9432  zeo  9434  zeo2  9435  zesq  10753  facndiv  10834  faclbnd  10836  faclbnd6  10839  bcxmas  11657  trireciplem  11668  odd2np1  12041  abssinper  15108  lgseisenlem1  15337  lgsquadlem1  15344