Theorem applamed ≪ | index | src | ≫ 

theorem applamed (G: wff) (b c: nat) {x: nat} (a: nat x):
  $ G /\ x = b -> a = c $ >
  $ G -> (\ x, a) @ b = c $;
StepHypRefExpression
1 applams 
(\ x, a) @ b = N[b / x] a
2 hyp e 
G /\ x = b -> a = c
3 2 sbned 
G -> N[b / x] a = c
4 1, 3 syl5eq 
G -> (\ 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)