How to prove that this sentence is true (phys chem)

'At equilibrium, the chemical potential of a component in the vapour must be the same as the chemical potential of that component in the fluid'

It also says that assume the Gibbs energy of a closed system at constant T and p is a minimum at equilibrium.

Just stuck on where to start of if it's easier than I think it is?
Thanks for any help

If the chemical components aren't the same then it won't be in equilibrium. If vapour is produced at a quicker rate than liquid then it isn't equilibrium

I think

That's what I thought but I think they want me to use an equation of some sort?
It also says 'change in Gibbs energy on moving Δn moles from phase α to phase β is given by ΔG = Δn[μ(β) - μ(α)]'

Christ, I haven't got a clue there, sorry. Thermodynamics not really my strong suit. What level is this?

Oh right no worries, bit of a long shot asking on here to be honest: it's 2nd year undergrad!