Does the following argument illustrate the Law of Syllogism?

Given: If the sun is shining, then it is a beautiful day.

If it is a beautiful day, then we will go for a bike ride.

Conclude: If the sun is shining, then we will go for a bike ride.

Law of Syllogism states that if A is equal to B and B is equal to C, then A must be equal to C.

Here, lets say - If the sun is shining be 'A', then it is a beautiful day be 'B' and then we will go for a bike ride be 'C'

Then according to the stated law, A equals B and B equals C, thus equaling A and C.