diff --git a/src/anyio/streams/tls.py b/src/anyio/streams/tls.py
index 83240b4d..b6961bee 100644
--- a/src/anyio/streams/tls.py
+++ b/src/anyio/streams/tls.py
@@ -162,9 +162,8 @@ async def _call_sslobject_method(
             except ssl.SSLError as exc:
                 self._read_bio.write_eof()
                 self._write_bio.write_eof()
-                if (
-                    isinstance(exc, ssl.SSLEOFError)
-                    or "UNEXPECTED_EOF_WHILE_READING" in exc.strerror
+                if isinstance(exc, ssl.SSLEOFError) or (
+                    exc.strerror and "UNEXPECTED_EOF_WHILE_READING" in exc.strerror
                 ):
                     if self.standard_compatible:
                         raise BrokenResourceError from exc