Theorem cnveqd ≪ | index | src | ≫

theorem cnveqd (_G: wff) (_A1 _A2: set):
  $ _G -> _A1 == _A2 $ >
  $ _G -> cnv _A1 == cnv _A2 $;

Step	Hyp	Ref	Expression
1		eqidd	_G -> y, x = y, x
2		hyp _Ah	_G -> _A1 == _A2
3	1, 2	eleqd	_G -> (y, x e. _A1 <-> y, x e. _A2)
4	3	abeqd	_G -> {y \| y, x e. _A1} == {y \| y, x e. _A2}
5	4	sabeqd	_G -> S\ x, {y \| y, x e. _A1} == S\ x, {y \| y, x e. _A2}
6	5	conv cnv	_G -> cnv _A1 == cnv _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)