Theorem peano2cn 8461

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4742. (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 8272	. 2 |- 1 e. CC
2		addcl 8304	. 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 6085   CCcc 8177   1c1 8180   + caddc 8182

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8272  ax-addcl 8275

This theorem is used by:  xp1d2m1eqxm1d2  9558  nneo  9749  zeo  9751  zeo2  9752  zesq  11096  facndiv  11177  faclbnd  11179  faclbnd6  11182  bcxmas  12256  trireciplem  12267  odd2np1  12640  abssinper  15947  lgseisenlem1  16189  lgsquadlem1  16196