Everyone who saw everything testified

Everyone who saw everything is such that (he or she testified)

(∀x: x is a person who saw everything) x testified

(∀x: x is a person ∧ x saw everything) x testified

(∀x: x is a person ∧ everything is such that (x saw it)) x testified

(∀x: x is a person ∧ ∀y x saw y) x testified

(∀x: Px ∧ ∀y Sxy) Tx

Everyone who saw anything testified

Everything is such that (everyone who saw it testified)

∀y everyone who saw y testified

∀y everyone who saw y is such that (he or she testified)

∀y (∀x: x is a person who saw y) x testified

∀y (∀x: x is a person ∧ x saw y) x testified

∀y (∀x: Px ∧ Sxy) Tx