Theorem sappslam | index | src |

theorem sappslam (B: set) (a: nat) {x: nat} (A: set x):
  $ x = a -> A == B $ >
  $ (\\ x, A) @@ a == B $;
StepHypRefExpression
1 eqstr
(\\ x, A) @@ a == S[a / x] A -> S[a / x] A == B -> (\\ x, A) @@ a == B
2 sappslams
(\\ x, A) @@ a == S[a / x] A
3 1, 2 ax_mp
S[a / x] A == B -> (\\ x, A) @@ a == B
4 hyp h
x = a -> A == B
5 4 sbse
S[a / x] A == B
6 3, 5 ax_mp
(\\ x, A) @@ a == B

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)