Theorem ocaseeq1d ≪ | index | src | ≫

theorem ocaseeq1d (_G: wff) (_z1 _z2: nat) (S: set):
  $ _G -> _z1 = _z2 $ >
  $ _G -> ocase _z1 S == ocase _z2 S $;

Step	Hyp	Ref	Expression
1		hyp _h	_G -> _z1 = _z2
2		eqsidd	_G -> S == S
3	1, 2	ocaseeqd	_G -> ocase _z1 S == ocase _z2 S

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)