Theorem oddeqd ≪ | index | src | ≫

theorem oddeqd (_G: wff) (_n1 _n2: nat):
  $ _G -> _n1 = _n2 $ >
  $ _G -> (odd _n1 <-> odd _n2) $;

Step	Hyp	Ref	Expression
1		hyp _nh	_G -> _n1 = _n2
2	1	modeq1d	_G -> _n1 % 2 = _n2 % 2
3	2	eqeq1d	_G -> (_n1 % 2 = 1 <-> _n2 % 2 = 1)
4	3	conv odd	_G -> (odd _n1 <-> odd _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), axs_peano (peano2, addeq, muleq)