Accessing internet on a MacBook Air through iPhone's access to Wi-Fi, rather than its access to cellular data
As per http://support.apple.com/kb/ht4517, you cannot use your Wi-Fi connection on your iPhone while using Wi-Fi for Personal Hotspot.


  If other devices have joined your Personal Hotspot using Wi-Fi, you can use only cellular data to connect to the Internet from the host device.


However, if you connect your computer to the iPhone using a USB cable or Bluetooth, it seems to be possible to utilise the Wi-Fi via the phone. In this case the blue statusbar informs the usage of Personal Hotspot connections and Wi-Fi icon is still visible on the iPhone.