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Arrow functions is not supported by IE 11. You need to polyfill all the ES6+ syntax to make it compatible with IE 11. You could use babel to polyfill the code in your question:
(void 0).$validator.validateAll().then(function (result) {
if (result) {
//submit
}
});
You could also refer to the accepted answer in this thread about installing and importing babel-polyfill
to make vue.js app compatible with IE 11.
Source:stackexchange.com