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# I need to prove the following conclusion xyz((Indiff(x,y)StrongPref(z,x))StrongPref(z,y)) using some OR all of the following premises:...

I need to prove the following conclusion ∀x∀y∀z((Indiff(x,y)∧StrongPref(z,x))→StrongPref(z,y)) using some OR all of the following premises:

P5: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x))

P6: ∀x∀y∀z((StrongPref(x,y)∧StrongPref(y,z))→StrongPref(x,z))

P7: ∀xIndiff(x,x)

P8: ∀x∀y(Indiff(x,y)→Indiff(y,x))

P9: ∀x∀y∀z((StrongPref(x,y)∧Indiff(y,z))→StrongPref(x,z))

P10: ∀x∀y(StrongPref(x,y)∨Indiff(x,y)∨StrongPref(y,x))

P11: ∀x∀y(WeakPref(x,y)↔(StrongPref(x,y)∨Indiff(x,y)))this has to be done using the FITCH program but i don't know how to do this