Pardon my ignorance, but I've been stuck with this silly problem for almost a whole day while trying to learn some quadratic forms theory. Let $F$ be a field of characteristic $\neq 2$. Szymiczek's book on the algebraic theory of quadratic forms contains an exercise where the equivalence of the following are supposed to be proven:

- $I^2(F)=0$.
- $\langle 1,a,b,ab\rangle=0\in W(F)$ for all $a,b\in F^\times$.
- $\langle 1,a,b,ab\rangle$ is hyperbolic.
- $\langle 1,a,b,ab\rangle$ is isotropic.
- $\langle 1,a\rangle$ is universal for all $a\in F^\times$.
- $\langle a,b\rangle$ is universal for all $a,b\in F^\times$.

For some reason I seem to have got stuck on showing $(4)\Rightarrow (5)\Rightarrow (6)$, everything else being trivial or easy.

EDIT: I actually have $(5)\Rightarrow (6)$ now, so I'm looking for $(4)\Rightarrow (5)$.