Help with travel adapter and voltage?

I bought a travel adapter (not a voltage converter, just a simple adapter) and it says "Suitable for small appliances and portable electronic equipment up to 1430w on the 110v system & up to 2990w on the 230v system."

I know that USA typically uses the 110v system and that my iPhone adapter (wall plug) is suitable for 100v-240v, but the travel adapter says maximum 230v.

Can I use it safely because my iPhone charger is dual voltage or is it unsafe because it goes up to 240v?

Yes, it's OK. "230 volt system" really means about 220-240 volts.

As long as it plugs in at both ends properly, the voltage is not an issue.

It's complicated.
Short version: you'll be ok.

Longer version: the nominal mains voltages across the globe vary between 100 and 240 Volts ( with varying permissible tolerances. Your plug adapter is likely rated for 15 Amps at 230V - but it still has to work safely at 253 Volts, which would be the maximum permissible voltage in Europe. I don't think you'll have to worry about the few countries which are using a (nominal) 240 V grid.