# Basic inequality

#### solakis

##### Active member
Prove:

$A\leq B\wedge B\leq A\Rightarrow A=B$

#### Country Boy

##### Well-known member
MHB Math Helper
Trichotomy: Given numbers A and B, one and only one must be true:
1) A> B
2) A< B
3) A= B

Since $$\displaystyle A\le B$$, A> B is not true.
Since $$\displaystyle B\le A$$, A< B is not true.

#### solakis

##### Active member
Is the trichotomy law you are using Equivelant to the following:
$A<B\vee B<A\vee A=B$