Theorem peano2cn 8054

Description: A theorem for complex numbers analogous the second Peano postulate peano2 4579. (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 7867	. 2 |- 1 e. CC
2		addcl 7899	. 2 |- ( ( A e. CC /\ 1 e. CC ) -> ( A + 1 ) e. CC )
3	1, 2	mpan2 423	1 |- ( A e. CC -> ( A + 1 ) e. CC )

Syntax hints:   -> wi 4   e. wcel 2141  (class class class)co 5853   CCcc 7772   1c1 7775   + caddc 7777

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-1cn 7867  ax-addcl 7870

This theorem is referenced by:  xp1d2m1eqxm1d2  9130  nneo  9315  zeo  9317  zeo2  9318  zesq  10594  facndiv  10673  faclbnd  10675  faclbnd6  10678  bcxmas  11452  trireciplem  11463  odd2np1  11832  abssinper  13561