In 'A Course in Universal Algebra' (Stanley Burris and H. P. Sankappanavar) definition 1.1 a lattice is presented to me as non-empty set $L$ together with binary operations $\wedge$ and $\vee$ that meet the following conditions:
1) $x\vee y=y\vee x$ and $x\wedge y=y\wedge x$
2) $x\vee\left(y\vee z\right)=\left(x\vee y\right)\vee z$ and $x\wedge\left(y\wedge z\right)=\left(x\wedge y\right)\wedge z$
3) $x\vee x=x$ and $x\wedge x=x$
4) $x\vee\left(x\wedge y\right)=x$ and $x\wedge\left(x\vee y\right)=x$
In exercise 1.2 it is asked to verify that condition 3) is a consequence of the conditions 1), 2) and 4).
I am stuck and humbly ask for help. Thanks in advance.
Let $x\vee x=s$. It follows from 4) $x\wedge s=x$. Hence $x\vee x=x\vee (x\wedge s)=x$ (again from 4)).