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Ψ (x)=<x|Ψ >=<x|∫dp|p><p|Ψ >=∫dp<x|p><p|Ψ>=∫dp exp{ipx/h}Ψ(p)

Ψ (p)=<p|Ψ >=∫dx exp{-ipx/h}Ψ(x)

Ψ (x)=<x|Ψ >=<x|∫dp|p><p|Ψ >=∫dp<x|p><p|Ψ>=∫dp exp{ipx/h}Ψ(p)

i don't understand how ∫dp<x|p><p|Ψ> become ∫dp exp{ipx/h}Ψ(p)

Could you please tell me the drivation of this formula?

and another question is why Ψ (x) could be denoted as <x|Ψ >?