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	⊢ 𝜑
Assertion	ainaiaandna	⊢ ( 𝜑 → ¬ ( 𝜑 → ( 𝜑 ∧ ¬ 𝜑 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ainaiaandna.1	⊢ 𝜑
2	1	atnaiana	⊢ ¬ ( 𝜑 → ( 𝜑 ∧ ¬ 𝜑 ) )
3	2	a1i	⊢ ( 𝜑 → ¬ ( 𝜑 → ( 𝜑 ∧ ¬ 𝜑 ) ) )