Theorem ifpos ≪ | index | src | ≫

pub theorem ifpos (p: wff) (a b: nat): $ p -> if p a b = a $;

Step	Hyp	Ref	Expression
1		ifppos	p -> (ifp p (n = a) (n = b) <-> n = a)
2	1	eqtheabd	p -> the {n \| ifp p (n = a) (n = b)} = a
3	2	conv if	p -> if p a b = 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)