Metamath Proof Explorer

Theorem ine1

Description: _i is not 1. (Contributed by SN, 25-Apr-2025)

Ref Expression
Assertion ine1 
|- _i =/= 1

Proof

Step Hyp Ref Expression
1 1re 
 |-  1 e. RR
2 inelr 
 |-  -. _i e. RR
3 nelne2 
 |-  ( ( 1 e. RR /\ -. _i e. RR ) -> 1 =/= _i )
4 1 2 3 mp2an 
 |-  1 =/= _i
5 4 necomi 
 |-  _i =/= 1