Enderton 2.5 problem 1.

(Semantic rule EI) Assume that the constant symbol does not occur in , or , and that . Show (without using the soundness and completeness theorems) that .

If I were able to use the soundness theorem, I could use the rule EI and apply the soundness theorem. However, it is not allowed to use the soundness theorem.

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Let A be a structure for the language and let such that if , then . Now it suffices to show that .

I can't proceed from here.

Any help will be appreciated.