Theorem Powereqd ≪ | index | src | ≫

theorem Powereqd (_G: wff) (_A1 _A2: set):
  $ _G -> _A1 == _A2 $ >
  $ _G -> Power _A1 == Power _A2 $;

Step	Hyp	Ref	Expression
1		eqsidd	_G -> x == x
2		hyp _Ah	_G -> _A1 == _A2
3	1, 2	sseqd	_G -> (x C_ _A1 <-> x C_ _A2)
4	3	abeqd	_G -> {x \| x C_ _A1} == {x \| x C_ _A2}
5	4	conv Power	_G -> Power _A1 == Power _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)