Theorem peano2cn 8468

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4744. (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 8278	. 2 |- 1 e. CC
2		addcl 8310	. 2 |- ( ( A e. CC /\ 1 e. CC ) -> ( A + 1 ) e. CC )
3	1, 2	mpan2 429	1 |- ( A e. CC -> ( A + 1 ) e. CC )

This proof depends on syntax axioms:   -> wi 4   e. wcel 2209  (class class class)co 6088   CCcc 8183   1c1 8186   + caddc 8188

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8278  ax-addcl 8281

This theorem is used by:  xp1d2m1eqxm1d2  9569  nneo  9760  zeo  9762  zeo2  9763  zesq  11117  facndiv  11199  faclbnd  11201  faclbnd6  11204  bcxmas  12281  trireciplem  12292  odd2np1  12665  abssinper  16073  lgseisenlem1  16394  lgsquadlem1  16401