Theorem trueeqd ≪ | index | src | ≫

theorem trueeqd (_G: wff) (_n1 _n2: nat):
  $ _G -> _n1 = _n2 $ >
  $ _G -> (true _n1 <-> true _n2) $;

Step	Hyp	Ref	Expression
1		hyp _nh	_G -> _n1 = _n2
2		eqidd	_G -> 0 = 0
3	1, 2	neeqd	_G -> (_n1 != 0 <-> _n2 != 0)
4	3	conv true	_G -> (true _n1 <-> true _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)