Theorem apprlam0 ≪ | index | src | ≫

theorem apprlam0 (a: nat) {x: nat} (b c: nat x):
  $ ~c e. a -> (\. x e. a, b) @ c = 0 $;

Step	Hyp	Ref	Expression
1		noteq	(c e. Dom (\. x e. a, b) <-> c e. a) -> (~c e. Dom (\. x e. a, b) <-> ~c e. a)
2		eleq2	Dom (\. x e. a, b) == a -> (c e. Dom (\. x e. a, b) <-> c e. a)
3		dmrlam	Dom (\. x e. a, b) == a
4	2, 3	ax_mp	c e. Dom (\. x e. a, b) <-> c e. a
5	1, 4	ax_mp	~c e. Dom (\. x e. a, b) <-> ~c e. a
6		ndmapp	~c e. Dom (\. x e. a, b) -> (\. x e. a, b) @ c = 0
7	5, 6	sylbir	~c e. a -> (\. x e. a, b) @ c = 0

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)