if ... then ... in Chinese without any special words
你 高兴，我 也 高兴。


I interpret it as "You are happy, and I am happy too." It means your happiness may not be necessarily relevant to mine, but they just happen simultaneously for some or no reason. 

Think about this similar sentence: 你有苹果，我也有苹果. It means you have an apple and I have one too. It doesn't mean if you have an apple then I have an apple too. There isn't any correlation here. 

"If you are happy then I am happy." is more like (如果)你高兴，我就高兴. 如果 in this case can be dropped. 

But if you say 如果你有苹果，我就有苹果， it clearly address the conditional relationship. It means both of us share the same prerequisite for getting an apple. So, if you can get one, then no doubt I can get one too. 

Hope this clear.