Theorem sappeq2d ≪ | index | src | ≫

theorem sappeq2d (_G: wff) (F: set) (_x1 _x2: nat):
  $ _G -> _x1 = _x2 $ >
  $ _G -> F @@ _x1 == F @@ _x2 $;

Step	Hyp	Ref	Expression
1		eqsidd	_G -> F == F
2		hyp _h	_G -> _x1 = _x2
3	1, 2	sappeqd	_G -> F @@ _x1 == F @@ _x2

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)