Theorem peano2cn 8154

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4627. (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 7965	. 2 |- 1 e. CC
2		addcl 7997	. 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 2164  (class class class)co 5918   CCcc 7870   1c1 7873   + caddc 7875

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-1cn 7965  ax-addcl 7968

This theorem is referenced by:  xp1d2m1eqxm1d2  9235  nneo  9420  zeo  9422  zeo2  9423  zesq  10729  facndiv  10810  faclbnd  10812  faclbnd6  10815  bcxmas  11632  trireciplem  11643  odd2np1  12014  abssinper  14981  lgseisenlem1  15186  lgsquadlem1  15191