Answering this question depends on what is meant by “equal.”  Peace and submission are certainly not logically equivalent.  One might wonder whether submission always brings peace and, again, the answer seems to be “no.”  As a counterexample, consider having to submit to a wicked tyrant.  Okay, then does peace always invovle submission? This is trickier to answer, since it revolves around considering what it means to submit and to what sorts of things one might submit. I'm not convinced that peace requires submission, but I'm sure one could always find a way to view it as involving a submission in some sense.

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