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 ) |
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 ) |