Theorem Taileqd ≪ | index | src | ≫

theorem Taileqd (_G: wff) (_S1 _S2: set):
  $ _G -> _S1 == _S2 $ >
  $ _G -> Tail _S1 == Tail _S2 $;

Step	Hyp	Ref	Expression
1		eqidd	_G -> suc n = suc n
2		hyp _Sh	_G -> _S1 == _S2
3	1, 2	eleqd	_G -> (suc n e. _S1 <-> suc n e. _S2)
4	3	abeqd	_G -> {n \| suc n e. _S1} == {n \| suc n e. _S2}
5	4	conv Tail	_G -> Tail _S1 == Tail _S2

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)