theorem rneqd (_G: wff) (_A1 _A2: set):
$ _G -> _A1 == _A2 $ >
$ _G -> Ran _A1 == Ran _A2 $;
Step | Hyp | Ref | Expression |
1 |
|
eqidd |
_G -> x, y = x, y |
2 |
|
hyp _Ah |
_G -> _A1 == _A2 |
3 |
1, 2 |
eleqd |
_G -> (x, y e. _A1 <-> x, y e. _A2) |
4 |
3 |
exeqd |
_G -> (E. x x, y e. _A1 <-> E. x x, y e. _A2) |
5 |
4 |
abeqd |
_G -> {y | E. x x, y e. _A1} == {y | E. x x, y e. _A2} |
6 |
5 |
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)