Your ISP can see you connected to the proxy domain over an encrypted TLS connection. They cannot see which sites you opened through it.
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When you use AnyProxy, your ISP sees exactly one thing: an encrypted HTTPS connection from your device to anyproxy.site (or its regional subdomain). The TLS handshake reveals the proxy hostname via SNI, but nothing about what happens inside that connection. So your ISP knows you visited the proxy site — same visibility they have for any website you load. They do not know which pages you opened through the proxy, what searches you ran, or what videos you watched. If you are in a country that specifically monitors or blocks proxy traffic (some regulated markets do), the connection itself may be visible as "user connected to a proxy". If that is a concern, obfuscated VPN protocols (V2Ray, Shadowsocks) are designed to disguise the connection as ordinary HTTPS to a random domain. For most users on ordinary networks, a web proxy over HTTPS is the appropriate privacy-vs-simplicity tradeoff.
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