Theorem rappsab ≪ | index | src | ≫ 

theorem rappsab {x: nat} (A: set x): $ (S\ x, A) @' x == A $;
StepHypRefExpression
1
 
(S\ x, A) @' a1 == S[a1 / x] A
2
 
a1 = x -> (S\ x, A) @' a1 == (S\ x, A) @' x
3
 
a1 = x -> x = a1
4
 
x = a1 -> A == S[a1 / x] A
5
 
x = a1 -> S[a1 / x] A == A
6
3, 5
 
a1 = x -> S[a1 / x] A == A
7
2, 6
 
a1 = x -> ((S\ x, A) @' a1 == S[a1 / x] A <-> (S\ x, A) @' x == A)
8
1, 7
 
(S\ 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)