Theorem peano2cn 8161

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4631. (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 7972	. 2 |- 1 e. CC
2		addcl 8004	. 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 5922   CCcc 7877   1c1 7880   + caddc 7882

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 7972  ax-addcl 7975

This theorem is referenced by:  xp1d2m1eqxm1d2  9244  nneo  9429  zeo  9431  zeo2  9432  zesq  10750  facndiv  10831  faclbnd  10833  faclbnd6  10836  bcxmas  11654  trireciplem  11665  odd2np1  12038  abssinper  15082  lgseisenlem1  15311  lgsquadlem1  15318