Saving Throws when mutliclasssing

[Ryallun]

Hi. Our group just started running our first 5th Edition campaign. Could anyone please enlighten me as to how Saving Throws work when you multi-class in 5th Edition please ?
Eg My Fighter1 wants to become Wizard @ level 2. As a Level 1 Fighter, his Saves are STR & CON. A Wizard gets Saving Throws of IQ & WIS. It seems too generous to add profieciency on those to his other Saves, but is that how it works in 5th Ed please ? Thanks for your help.

[Thegroo]

You are only proficient in the saving throws of your starting class.

You also don't gain any new skills.

In the PHB p. 163 is a table of what you get when multiclassing into a new class