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## Homework Statement

Trying to prove some of the basic laws in set theory, and would like any opinions on 1 of my proofs (eg hints on how can I improve it, is it even a valid proof). Thanks in advance.

[tex](A \subseteq B \wedge B \subseteq C) \rightarrow (A \subseteq C)[/tex]

## Homework Equations

## The Attempt at a Solution

1) [tex]\forall x \in A, x \in B$[/tex] - definition of a subset

2) [tex]\forall x \in B, x \in C[/tex] - definition of a subset

3) [tex]\forall x \in A, x \in C[/tex] - 1, 2

4) [tex]A \subseteq C[/tex] - 3, definition of a subset