simptcheck formal version of this item

Satallax
Satallax is a higher-order
automated theorem prover.
Satallax won the THF division
of CASC-23 in 2011.

Scunak

Impressum
Contact Person
Chad E Brown

Theorem

Let A be an object. Let X and Y be members of ℘(A). Assume for all a ∈ A a∈X implies a∈Y. Then we have X⊆Y.

Background

The following background is necessary to understand this theorem.

(.) Let A and x be objects. Then x∈A is a proposition.

(.) Let A be an object. Then ℘(A) is an object.

(.) Let A and B be objects. Then "A⊆B" is a proposition.

Background for Proof

The following background is necessary for the proof.

(.) Let A, B and x be objects. Assume B∈℘(A) and x∈B. Then we know x∈A.

(.) Let A and B be objects. Assume for all x x∈A implies x∈B. Then we know A⊆B.

Proof

Trivial.

Click here to modify variable names (JavaScript Must Be Enabled).

Hide Background.

Test yourself on this item.

See Also

Theorem Theorem Theorem Theorem Theorem Theorem Theorem Theorem