Metamath Proof Explorer

Theorem ltned

Description: 'Greater than' implies not equal. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypotheses ltd.1 
|- ( ph -> A e. RR )
ltned.2 
|- ( ph -> A < B )
Assertion ltned 
|- ( ph -> A =/= B )

Proof

Step Hyp Ref Expression
1 ltd.1 
 |-  ( ph -> A e. RR )
2 ltned.2 
 |-  ( ph -> A < B )
3 1 2 gtned 
 |-  ( ph -> B =/= A )
4 3 necomd 
 |-  ( ph -> A =/= B )