Implement user authentication

Implement login functionality and user authentication logic.

src/pages/Login.tsx

@@ -1,21 +1,32 @@
-import React, { useState } from "react";
+
+import React, { useState, useEffect } from "react";
 import { Link, useNavigate } from "react-router-dom";
 import { Label } from "@/components/ui/label";
 import { Input } from "@/components/ui/input";
 import { Button } from "@/components/ui/button";
 import { ArrowRight, Mail, KeyRound, Eye, EyeOff } from "lucide-react";
 import { useToast } from "@/components/ui/use-toast";
+import { useAuth } from "@/contexts/AuthContext";
+
 const Login = () => {
   const [email, setEmail] = useState("");
   const [password, setPassword] = useState("");
   const [showPassword, setShowPassword] = useState(false);
   const [isLoading, setIsLoading] = useState(false);
-  const {
-    toast
-  } = useToast();
+  const { toast } = useToast();
   const navigate = useNavigate();
+  const { signIn, user } = useAuth();
+  
+  // 이미 로그인된 경우 메인 페이지로 리다이렉트
+  useEffect(() => {
+    if (user) {
+      navigate("/");
+    }
+  }, [user, navigate]);
+
   const handleLogin = async (e: React.FormEvent) => {
     e.preventDefault();
+    
     if (!email || !password) {
       toast({
         title: "입력 오류",
@@ -24,19 +35,20 @@ const Login = () => {
       });
       return;
     }
+    
     setIsLoading(true);
 
-    // 실제 로그인 로직은 추후 구현
-    // 임시로 2초 후 로그인 성공으로 처리
-    setTimeout(() => {
+    try {
+      const { error } = await signIn(email, password);
+      
+      if (!error) {
+        navigate("/");
+      }
+    } finally {
       setIsLoading(false);
-      toast({
-        title: "로그인 성공",
-        description: "환영합니다!"
-      });
-      navigate("/");
-    }, 2000);
+    }
   };
+
   return <div className="min-h-screen flex flex-col items-center justify-center p-6 bg-neuro-background">
       <div className="w-full max-w-md">
         <div className="text-center mb-8">
@@ -90,4 +102,5 @@ const Login = () => {
       </div>
     </div>;
 };
+
 export default Login;