A lattice is an algebraic structure $(L, \wedge, \vee)$, consisting of a set $L$ and two binary, commutative and associative operations $\wedge$ and $\vee$ on $L$ satisfying the following identities for all $a,b \in L$:
ABS1: $a \wedge (a \vee b) = a$
ABS2: $a \vee (a \wedge b) = a$
A lattice $(L, \wedge, \vee)$ is distributive if it satisfies one of the following identities for all $a,b,c \in L$:
DISTR1: $a \wedge (b \vee c) = (a \wedge b) \vee (a \wedge c)$
DISTR2: $a \vee (b \wedge c) = (a \vee b) \wedge (a \vee c)$
How can I prove that a lattice that satisfies DISTR1 satisfies also DISTR2?
Edit: I can write $$\begin{align}a \vee (b \wedge c) &= (a \vee (a \wedge c)) \vee (b \wedge c) \\&= a \vee ((a \wedge c) \vee (b \wedge c)) \\&= a \vee ((c \wedge a) \vee (c \wedge b)) \\&= a \vee (c \wedge (a \vee b))\end{align}$$ But I don't know how to conclude...