He is overjoyed that he is going to be a father. 中 that 所引導的是名詞子句。因為that子句不受介系詞的管束 ，所以當主詞補語的overjoyed後面的介系詞遭強制刪去。因為在結構上that子句原來是要當介系詞的受詞，雖然介系詞遭刪，我們界定其為名詞子句。
He is overjoyed at the news. = 他聽到那消息而欣喜若狂。(overjoyed是屬於後面要用介系詞，然後才接名詞當受詞的形容詞，the news是介系詞at的受詞）
He was overjoyed that he saw me. =他非常高興看到我。（介系詞因為that子句而遭強制刪去）
後面接介系詞再接名詞為受詞的形容詞有：afraid, angry, aware, certain, happy, proud, sad, sorry, amused, annoyed, astonished, convinced, pleased, shocked等，但在受詞為that子句時，通常介系詞會遭強制刪除。
如：He is afraid of snakes.
I was afraid of getting lost.
I was afraid that I might die.
He warned me of their wicked design.
I warn you that it is dangerous.(that子句前的介系詞遭強制刪去）
I'm lucky in that I have three brothers.
Airline officials had nothnig to tell us except that the flight had been delayed.
R.A Close所著A Reference Grammar for Students of English p.77
2013-12-18 12:54:51 補充：
Success comes to whoever is ready for it.
Aren't you concerned about how long it will take?
I can't rely on what you tell me.
We'll find out whether it turns out to be a good idea or bad idea.
2013-12-18 13:06:52 補充：
更正：Airline officials had nothnig to tell us except that the flight had been delayed.