The demand function ${\displaystyle x(p,w)}$ satisfies the weak axiom of revealed preference if:
${\displaystyle \forall (p,w),(p^{\prime },w^{\prime }){\mbox{ if }}px(p^{\prime },w^{\prime })\leq w{\mbox{ and }}x(p^{\prime },w^{\prime })\neq x({p},{w}){\mbox{ then }}p^{\prime }x({p},{w})>w^{\prime }}$
The consumer faced with ${\displaystyle (p,w)}$ could have chosen $\funcd{x}{p^{\prime},w^{\prime}}$ but chose ${\displaystyle x(p,w)}$, assuming the consumer chooses consistently, if $\funcd{x}{p^{\prime},\primd{w}}$ is ever chosen, ${\displaystyle x(p,w)}$ must not be affordable. Hence, ${\displaystyle p^{\prime }\cdot x(p,w)>w^{\prime }}$