Theorem addlass ≪ | index | src | ≫

theorem addlass (a b c: nat): $ a + (b + c) = b + (a + c) $;

Step	Hyp	Ref	Expression
1		eqtr3	a + b + c = a + (b + c) -> a + b + c = b + (a + c) -> a + (b + c) = b + (a + c)
2		addass	a + b + c = a + (b + c)
3	1, 2	ax_mp	a + b + c = b + (a + c) -> a + (b + c) = b + (a + c)
4		eqtr	a + b + c = b + a + c -> b + a + c = b + (a + c) -> a + b + c = b + (a + c)
5		addeq1	a + b = b + a -> a + b + c = b + a + c
6		addcom	a + b = b + a
7	5, 6	ax_mp	a + b + c = b + a + c
8	4, 7	ax_mp	b + a + c = b + (a + c) -> a + b + c = b + (a + c)
9		addass	b + a + c = b + (a + c)
10	8, 9	ax_mp	a + b + c = b + (a + c)
11	3, 10	ax_mp	a + (b + c) = b + (a + 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_peano (peano2, peano5, addeq, add0, addS)