Theorem sappeq1d ≪ | index | src | ≫ 

theorem sappeq1d (_G: wff) (_F1 _F2: set) (x: nat):
  $ _G -> _F1 == _F2 $ >
  $ _G -> _F1 @@ x == _F2 @@ x $;
StepHypRefExpression
1 hyp _h 
_G -> _F1 == _F2
2 eqidd 
_G -> x = x
3 1, 2 sappeqd 
_G -> _F1 @@ x == _F2 @@ x

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 (peano2, addeq, muleq)