Contains everything

This is a set theory based language, Initially designed by C++DSUCKER (talk) but with the logical operator removed with help of uni on discord (though these changes did not make it into the final language). the original used nand but i eventually went with implies as false is constructible.

It was designed to be as simple as possible.

Instructions

Instruction	Description
(∀x.P)	if predicate P is True for all sets x then True else False
(a∈b)	if a contains b then True else False
(A→B)	A implies B

Examples

False

(∀x.(x∈x))

True

(∀x.((x∈x)→(x∈x)))

Invert predicate P

(P→(∀x.(x∈x)))

is x the empty set?

(∀v.((x∈v)→(∀t.(t∈t)))) golfed: (∀v.((x∈v)→(v∈v)))

are x and y equal?

(∀v.(((((x∈v)→(y∈v))→(v∈v))→((y∈v)→(x∈v)))→(v∈v)))

Exists x such that P is true

(((∀x.(P→(x∈x)))→(∀v.(v∈v)))