Theorem applam | index | src |

theorem applam {x: nat} (a: nat x): $ (\ x, a) @ x = a $;
StepHypRefExpression
1 eqtr
(\ x, a) @ x = N[x / x] a -> N[x / x] a = a -> (\ x, a) @ x = a
2 applams
(\ x, a) @ x = N[x / x] a
3 1, 2 ax_mp
N[x / x] a = a -> (\ x, a) @ x = a
4 sbnid
N[x / x] a = a
5 3, 4 ax_mp
(\ x, a) @ x = 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)