Theorem nseqd ≪ | index | src | ≫

theorem nseqd (_G: wff) (_a1 _a2: nat):
  $ _G -> _a1 = _a2 $ >
  $ _G -> _a1 == _a2 $;


_G -> _a1 = _a2
_G -> x = x
_G -> shr _a1 x = shr _a2 x
_G -> (odd (shr _a1 x) <-> odd (shr _a2 x))
_G -> {x | odd (shr _a1 x)} == {x | odd (shr _a2 x)}
_G -> _a1 == _a2

Step	Hyp	Ref	Expression
1		hyp _ah	_G -> _a1 = _a2
2		eqidd	_G -> x = x
3	1, 2	shreqd	_G -> shr _a1 x = shr _a2 x
4	3	oddeqd	_G -> (odd (shr _a1 x) <-> odd (shr _a2 x))
5	4	abeqd	_G -> {x \| odd (shr _a1 x)} == {x \| odd (shr _a2 x)}
6	5	conv ns	_G -> _a1 == _a2

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)