Theorem nfnot ≪ | index | src | ≫

theorem nfnot {x: nat} (a: wff x): $ F/ x a $ > $ F/ x ~a $;

Step	Hyp	Ref	Expression
1		con1	(~A. x ~a -> a) -> ~a -> A. x ~a
2		eal	A. x a -> a
3		con1	(~A. x a -> A. x ~A. x a) -> ~A. x ~A. x a -> A. x a
4		ax_10	~A. x a -> A. x ~A. x a
5	3, 4	ax_mp	~A. x ~A. x a -> A. x a
6		hyp h	F/ x a
7	6	nfi	a -> A. x a
8	7	eximi	E. x a -> E. x A. x a
9	8	conv ex	~A. x ~a -> ~A. x ~A. x a
10	5, 9	syl	~A. x ~a -> A. x a
11	2, 10	syl	~A. x ~a -> a
12	1, 11	ax_mp	~a -> A. x ~a
13	12	nfri	F/ x ~a

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_12)