 Consider a pair of ground formulas formula_36 and formula_37 whose extensions formula_38 and formula_39 (where the underscore here denotes the null context) are objects of the base topos.Then formula_36 implies formula_37 iff there is a monic from formula_38 to formula_39.If these are the case then, by theorem, the formula formula_37 is true in the slice formula_45, because the terminal object formula_46 of the slice factors through its extension formula_39.