Theorem Optioneqd ≪ | index | src | ≫

theorem Optioneqd (_G: wff) (_A1 _A2: set):
  $ _G -> _A1 == _A2 $ >
  $ _G -> Option _A1 == Option _A2 $;

Step	Hyp	Ref	Expression
1		biidd	_G -> (n = 0 <-> n = 0)
2		eqidd	_G -> n - 1 = n - 1
3		hyp _Ah	_G -> _A1 == _A2
4	2, 3	eleqd	_G -> (n - 1 e. _A1 <-> n - 1 e. _A2)
5	1, 4	oreqd	_G -> (n = 0 \/ n - 1 e. _A1 <-> n = 0 \/ n - 1 e. _A2)
6	5	abeqd	_G -> {n \| n = 0 \/ n - 1 e. _A1} == {n \| n = 0 \/ n - 1 e. _A2}
7	6	conv Option	_G -> Option _A1 == Option _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)