Theorem booleqd ≪ | index | src | ≫

theorem booleqd (_G: wff) (_n1 _n2: nat):
  $ _G -> _n1 = _n2 $ >
  $ _G -> (bool _n1 <-> bool _n2) $;

Step	Hyp	Ref	Expression
1		hyp _nh	_G -> _n1 = _n2
2		eqidd	_G -> 2 = 2
3	1, 2	lteqd	_G -> (_n1 < 2 <-> _n2 < 2)
4	3	conv bool	_G -> (bool _n1 <-> bool _n2)

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7), axs_peano (peano2, addeq)