Theorem ifid ≪ | index | src | ≫

theorem ifid (a: nat) (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), axs_the (theid)