Metamath Proof Explorer

Theorem peano2rem

Description: "Reverse" second Peano postulate analogue for reals. (Contributed by NM, 6-Feb-2007)

Ref Expression
Assertion peano2rem 
|- ( N e. RR -> ( N - 1 ) e. RR )

Proof

Step Hyp Ref Expression
1 1re 
 |-  1 e. RR
2 resubcl 
 |-  ( ( N e. RR /\ 1 e. RR ) -> ( N - 1 ) e. RR )
3 1 2 mpan2 
 |-  ( N e. RR -> ( N - 1 ) e. RR )