Theorem pi12eqd ≪ | index | src | ≫

theorem pi12eqd (_G: wff) (_n1 _n2: nat):
  $ _G -> _n1 = _n2 $ >
  $ _G -> pi12 _n1 = pi12 _n2 $;

Step	Hyp	Ref	Expression
1		hyp _nh	_G -> _n1 = _n2
2	1	fsteqd	_G -> fst _n1 = fst _n2
3	2	sndeqd	_G -> snd (fst _n1) = snd (fst _n2)
4	3	conv pi12	_G -> pi12 _n1 = pi12 _n2

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)