Theorem nateqd ≪ | index | src | ≫

theorem nateqd (_G _p1 _p2: wff):
  $ _G -> (_p1 <-> _p2) $ >
  $ _G -> nat _p1 = nat _p2 $;

Step	Hyp	Ref	Expression
1		hyp _ph	_G -> (_p1 <-> _p2)
2		eqidd	_G -> 1 = 1
3		eqidd	_G -> 0 = 0
4	1, 2, 3	ifeqd	_G -> if _p1 1 0 = if _p2 1 0
5	4	conv nat	_G -> nat _p1 = nat _p2

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)