Theorem applame ≪ | index | src | ≫

theorem applame (b c: nat) {x: nat} (a: nat x):
  $ x = b -> a = c $ >
  $ (\ x, a) @ b = c $;

Step	Hyp	Ref	Expression
1		eqtr	(\ x, a) @ b = N[b / x] a -> N[b / x] a = c -> (\ x, a) @ b = c
2		applams	(\ x, a) @ b = N[b / x] a
3	1, 2	ax_mp	N[b / x] a = c -> (\ x, a) @ b = c
4		hyp e	x = b -> a = c
5	4	sbne	N[b / x] a = c
6	3, 5	ax_mp	(\ x, a) @ b = c

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)