Mathematically stating geometric axioms

[colerelm]

How could I restate these statements using predicate logic? I am trying to state these axioms using less english and more mathematical notation:

Incidence Axiom 1. For every pair of distinct points P and Q there is exactly one line L
such that P and Q lie on L.

Incidence Axiom 2. For every line L there exist at least two distinct points P and Q such
that both P and Q lie on L.

Incidence Axiom 3. There exist three points that do not all lie on any one line.

Thanks in advance

 

[stapel]

A good start might be to clearly restate the axioms in logical language (for instance, as clear "if-then" statements), and to replace "for all" with the appropriate logical symbol.