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	|- ph
Assertion	ainaiaandna	|- ( ph -> -. ( ph -> ( ph /\ -. ph ) ) )

Proof

Step	Hyp	Ref	Expression
1		ainaiaandna.1	|- ph
2	1	atnaiana	|- -. ( ph -> ( ph /\ -. ph ) )
3	2	a1i	|- ( ph -> -. ( ph -> ( ph /\ -. ph ) ) )