Theorem peano2cn 8094

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4596. (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 7906	. 2 |- 1 e. CC
2		addcl 7938	. 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 2148  (class class class)co 5877   CCcc 7811   1c1 7814   + caddc 7816

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 7906  ax-addcl 7909

This theorem is referenced by:  xp1d2m1eqxm1d2  9173  nneo  9358  zeo  9360  zeo2  9361  zesq  10641  facndiv  10721  faclbnd  10723  faclbnd6  10726  bcxmas  11499  trireciplem  11510  odd2np1  11880  abssinper  14306  lgseisenlem1  14489