Theorem peano2cn 8373

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4699. (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 8185	. 2 |- 1 e. CC
2		addcl 8217	. 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 6028   CCcc 8090   1c1 8093   + caddc 8095

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 8185  ax-addcl 8188

This theorem is referenced by:  xp1d2m1eqxm1d2  9456  nneo  9644  zeo  9646  zeo2  9647  zesq  10983  facndiv  11064  faclbnd  11066  faclbnd6  11069  bcxmas  12130  trireciplem  12141  odd2np1  12514  abssinper  15657  lgseisenlem1  15889  lgsquadlem1  15896