Metamath Proof Explorer

Theorem eluz2b3

Description: Two ways to say "an integer greater than or equal to 2." (Contributed by Paul Chapman, 23-Nov-2012)

Ref Expression
Assertion eluz2b3 
|- ( N e. ( ZZ>= ` 2 ) <-> ( N e. NN /\ N =/= 1 ) )

Proof

Step Hyp Ref Expression
1 eluz2b2 
 |-  ( N e. ( ZZ>= ` 2 ) <-> ( N e. NN /\ 1 < N ) )
2 nngt1ne1 
 |-  ( N e. NN -> ( 1 < N <-> N =/= 1 ) )
3 2 pm5.32i 
 |-  ( ( N e. NN /\ 1 < N ) <-> ( N e. NN /\ N =/= 1 ) )
4 1 3 bitri 
 |-  ( N e. ( ZZ>= ` 2 ) <-> ( N e. NN /\ N =/= 1 ) )