Theorem rneqd ≪ | index | src | ≫

theorem rneqd (_G: wff) (_A1 _A2: set):
  $ _G -> _A1 == _A2 $ >
  $ _G -> Ran _A1 == Ran _A2 $;

Step	Hyp	Ref	Expression
1		hyp _Ah	_G -> _A1 == _A2
2	1	eleq2d	_G -> (x, y e. _A1 <-> x, y e. _A2)
3	2	exeqd	_G -> (E. x x, y e. _A1 <-> E. x x, y e. _A2)
4	3	abeqd	_G -> {y \| E. x x, y e. _A1} == {y \| E. x x, y e. _A2}
5	4	conv Ran	_G -> Ran _A1 == Ran _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)