6 that is (to say) 和i.e. 为什么可以连接两个句子
下面这三个句子应该都是对的：
He sacrifices himself to his country, that is (to say), he is a hero.
I'll meet you in the city, that is, I will if the trains are running.
I am a vegan, i.e., I do not eat any animal-based products.
这种语法现象该怎么解释呢？that is (to say) 和i.e.是起到了类似连词的作用？前后是主从句关系？
这种情况在插入语中并不普遍吧？比如 on the contrary或者for example等就不能如此使用。
谢谢老师！
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