This is a deductive argument in which the premises do support the conclusion. Furthermore, the premises are actually true. (Their truth is, usually, established by some discipline other than logic.) So, that the conclusion is actually true follows by inference from the premises (and NOT because it is known independently of studying the argument).

Consider:

The president of the United States must be 35 years of age or older.
George W. Bush is president of the United States.
So, George W. Bush must be 35 years of age or older.

If George W. Bush is president of the United States, then George W. Bush must be 35 years of age or older.
George W. Bush is president of the United States.
So, George W. Bush must be 35 years of age or older.

For either argument, the logic is valid. And, both the premises and the conclusion are true. Indeed, by definition, any valid argument with true premises will also have a true conclusion.