Theorem sbseh | index | src |

theorem sbseh {x: nat} (a: nat) (A B: set x):
  $ FS/ x B $ >
  $ x = a -> A == B $ >
  $ S[a / x] A == B $;
StepHypRefExpression
1 hyp h
FS/ x B
2 1 sbseht
A. x (x = a -> A == B) -> S[a / x] A == B
3 hyp e
x = a -> A == B
4 3 ax_gen
A. x (x = a -> A == B)
5 2, 4 ax_mp
S[a / x] 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)