Theorem ainaiaandna

Description: Given a, a implies it is not the case a implies a self contradiction. (Contributed by Jarvin Udandy, 7-Sep-2020)

	Ref	Expression
Hypothesis	ainaiaandna.1	$$⊢\phi$$
Assertion	ainaiaandna	$$⊢\phi \to \neg \left(\phi \to \left(\phi \wedge \neg \phi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		ainaiaandna.1	$$⊢\phi$$
2	1	atnaiana	$$⊢\neg \left(\phi \to \left(\phi \wedge \neg \phi \right)\right)$$
3	2	a1i	$$⊢\phi \to \neg \left(\phi \to \left(\phi \wedge \neg \phi \right)\right)$$