Theorem appendSi ≪ | index | src | ≫

theorem appendSi (a b c x: nat): $ a ++ b = c $ > $ x : a ++ b = x : c $;

Step	Hyp	Ref	Expression
1		eqtr	x : a ++ b = x : (a ++ b) -> x : (a ++ b) = x : c -> x : a ++ b = x : c
2		appendS	x : a ++ b = x : (a ++ b)
3	1, 2	ax_mp	x : (a ++ b) = x : c -> x : a ++ b = x : c
4		conseq2	a ++ b = c -> x : (a ++ b) = x : c
5		hyp h	a ++ b = c
6	4, 5	ax_mp	x : (a ++ b) = x : c
7	3, 6	ax_mp	x : a ++ b = x : 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)