R (x): x is a real number; N (x): x is a natural number, and z (x): x is an integer.
Premise: Ex(R(x)∧N(x)), Ax(N(x)→Z(x)).
Conclusion: Ex(R(x)∧Z(x)).
Prove:
① Ex(R(x)∧N(x)) *****
② R(a)∧N(a) ******
③ Not applicable.
④ Ax(N(x)→Z(x))
⑤ N(a)→Z(a)
⑥ Z(a)
⑦ R(a)
⑧ R(a)∧Z(a)
⑨ Ex(R(x)∧Z(x))
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Note: I leave the reasons behind each sentence to you.