grammar - and so's my wife

I'm tall, and so's my wife.

I looking for some way of understanding this kind of and so construction. Is it equivalent to the following?

I'm tall, and tall is my wife.

You could say, alternatively:

I'm tall, and my wife is tall.
I'm tall, and my wife is also.
I'm tall, and also my wife is. (maybe???)

So why is the 'is' moved before 'my wife" with the and so construction?