theorem reseqd (_G: wff) (_A1 _A2 _B1 _B2: set):
$ _G -> _A1 == _A2 $ >
$ _G -> _B1 == _B2 $ >
$ _G -> _A1 |` _B1 == _A2 |` _B2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
hyp _Ah |
_G -> _A1 == _A2 |
| 2 |
|
hyp _Bh |
_G -> _B1 == _B2 |
| 3 |
|
eqsidd |
_G -> _V == _V |
| 4 |
2, 3 |
xpeqd |
_G -> Xp _B1 _V == Xp _B2 _V |
| 5 |
1, 4 |
ineqd |
_G -> _A1 i^i Xp _B1 _V == _A2 i^i Xp _B2 _V |
| 6 |
5 |
conv res |
_G -> _A1 |` _B1 == _A2 |` _B2 |
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)