Am I properly connected to Wi-Fi?

I have an iPhone 5 and on the Wi-Fi tab it says the name of my Wi-Fi (which is out last name) so I'm assuming I'm connected? It doesn't say 'not connected' so that means it works? Right?

It means iphone sucks throw it out

Well have you tried browsing the internet? For example Facebook, Twitter, Instagram, if it's all loading than yes it's working.

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