Is the statement of one who says, "And by God, I have one like it," while believing so, then discovers he has left it at home, considered a binding oath that necessitates expiation, or is it a vain oath (laghw al-yamin)?

Whoever swears an oath about something, believing it to be as he swore, but it turns out not to be so, owes no expiation. This is considered a vain oath (laghw al-yameen), based on the words of Allah the Almighty: "Allah will not impose blame upon you for what is unintentional in your oaths, but He will impose blame upon you for what your hearts have earned. And Allah is Forgiving and Forbearing."