Metamath Proof Explorer

Theorem peano2re

Description: A theorem for reals analogous the second Peano postulate peano2nn . (Contributed by NM, 5-Jul-2005)

Ref Expression
Assertion peano2re 
|- ( A e. RR -> ( A + 1 ) e. RR )

Proof

Step Hyp Ref Expression
1 1re 
 |-  1 e. RR
2 readdcl 
 |-  ( ( A e. RR /\ 1 e. RR ) -> ( A + 1 ) e. RR )
3 1 2 mpan2 
 |-  ( A e. RR -> ( A + 1 ) e. RR )