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To thine own self be true, and it must follow, as the night the day, thou canst not then be false to any man. William Shakespeare

Please explain the meaning of above quotation in simple words.
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If you live your life according to the (high) standards you set for yourself, and therefore are honest with yourself, you will also live a life of honesty as it relates to other people.
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To thine own self be true: you must be true to yourself

it must follow, as the night the day: then it logically follows, as the night follows the day, that ....
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I need step by step explanation of this quotation:

To thine own self be true, and it must follow, as the night the day, thou canst not then be false to any man.

To thine (subject) own self be true, and it must follow, as the night the day, thou (subject) canst (can) not then be false to any man.

What does to thine mean? I think thine is being used as subject.

What does it must follow, as the night the day mean?

 Marius Hancu's reply was promoted to an answer.
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Jackson, the implied subject is the person being addressed - the "you" (or "thou") that is only mentioned later in the passage.

You must be true to (honest with) yourself. I guess that makes "thine own self" (yourself) the indirect object of your "trueness" (honesty).

"To thine own self" means simply "to yourself." Don't try to break out "To thine" from the rest.