Theorem peano2cn 8033

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4572. (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 7846	. 2 |- 1 e. CC
2		addcl 7878	. 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 2136  (class class class)co 5842   CCcc 7751   1c1 7754   + caddc 7756

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-1cn 7846  ax-addcl 7849

This theorem is referenced by:  xp1d2m1eqxm1d2  9109  nneo  9294  zeo  9296  zeo2  9297  zesq  10573  facndiv  10652  faclbnd  10654  faclbnd6  10657  bcxmas  11430  trireciplem  11441  odd2np1  11810  abssinper  13407