Theorem peano2cn 8313

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4693. (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 8124	. 2 |- 1 e. CC
2		addcl 8156	. 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 2202  (class class class)co 6017   CCcc 8029   1c1 8032   + caddc 8034

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8124  ax-addcl 8127

This theorem is referenced by:  xp1d2m1eqxm1d2  9396  nneo  9582  zeo  9584  zeo2  9585  zesq  10919  facndiv  11000  faclbnd  11002  faclbnd6  11005  bcxmas  12049  trireciplem  12060  odd2np1  12433  abssinper  15569  lgseisenlem1  15798  lgsquadlem1  15805