Metamath Proof Explorer

Theorem peano2cn

Description: A theorem for complex numbers analogous the second Peano postulate peano2nn . (Contributed by NM, 17-Aug-2005)

Ref Expression
Assertion peano2cn 
|- ( A e. CC -> ( A + 1 ) e. CC )

Proof

Step Hyp Ref Expression
1 ax-1cn 
 |-  1 e. CC
2 addcl 
 |-  ( ( A e. CC /\ 1 e. CC ) -> ( A + 1 ) e. CC )
3 1 2 mpan2 
 |-  ( A e. CC -> ( A + 1 ) e. CC )