Theorem Ifid ≪ | index | src | ≫

theorem Ifid (A: set) (p: wff): $ If p A A == A $;

Step	Hyp	Ref	Expression
1		Ifpos	p -> If p A A == A
2		Ifneg	~p -> If p A A == A
3	1, 2	cases	If p A A == A

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp, itru), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12), axs_set (elab, ax_8)