Theorem peano2cn 8455

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4740. (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 8266	. 2 |- 1 e. CC
2		addcl 8298	. 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 6079   CCcc 8171   1c1 8174   + caddc 8176

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8266  ax-addcl 8269

This theorem is used by:  xp1d2m1eqxm1d2  9541  nneo  9732  zeo  9734  zeo2  9735  zesq  11079  facndiv  11160  faclbnd  11162  faclbnd6  11165  bcxmas  12239  trireciplem  12250  odd2np1  12623  abssinper  15930  lgseisenlem1  16172  lgsquadlem1  16179