It is not a conditional at all ) If = "Because": Because he invited you, you should go. You should go because he invited you.
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MrPedantic1. If he invited you, you should go.
The speaker here assumes the truth of the statement in the if-clause: the purpose is not to present a hypothesis, but to draw an inference from an accepted fact.
"If" therefore has a meaning that is close to "since", as Ant suggests.
In this sentence, "if" may very well have the meaning
MrPedanticIn cases like #3, it seems to me, "should" is not entirely comfortable.
MrPedanticThough the forms are the same, "invited" in #1 is indicative (past simple); in #3, subjunctive.Right. I always get a bit confused about what is and isn't a subjunctive, but that makes sense.