Theorem peano2cn 7993

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4552. (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 7808	. 2 |- 1 e. CC
2		addcl 7840	. 2 |- ( ( A e. CC /\ 1 e. CC ) -> ( A + 1 ) e. CC )
3	1, 2	mpan2 422	1 |- ( A e. CC -> ( A + 1 ) e. CC )

Syntax hints:   -> wi 4   e. wcel 2128  (class class class)co 5818   CCcc 7713   1c1 7716   + caddc 7718

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-1cn 7808  ax-addcl 7811

This theorem is referenced by:  xp1d2m1eqxm1d2  9068  nneo  9250  zeo  9252  zeo2  9253  zesq  10518  facndiv  10595  faclbnd  10597  faclbnd6  10600  bcxmas  11368  trireciplem  11379  odd2np1  11745  abssinper  13127