Theorem dmrlam ≪ | index | src | ≫

theorem dmrlam {x: nat} (a b: nat x): $ Dom (\. x e. a, b) == a $;

Step	Hyp	Ref	Expression
1		eqstr	Dom (\. x e. a, b) == Dom ((\ x, b) \|` a) -> Dom ((\ x, b) \|` a) == a -> Dom (\. x e. a, b) == a
2		dmeq	\. x e. a, b == (\ x, b) \|` a -> Dom (\. x e. a, b) == Dom ((\ x, b) \|` a)
3		rlameqs	\. x e. a, b == (\ x, b) \|` a
4	2, 3	ax_mp	Dom (\. x e. a, b) == Dom ((\ x, b) \|` a)
5	1, 4	ax_mp	Dom ((\ x, b) \|` a) == a -> Dom (\. x e. a, b) == a
6		dmreslam	Dom ((\ x, b) \|` a) == a
7	5, 6	ax_mp	Dom (\. x e. 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, the0), axs_peano (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)