theorem cbvabh {x y: nat} (p q: wff x y):
$ F/ y p $ >
$ F/ x q $ >
$ x = y -> (p <-> q) $ >
$ {x | p} == {y | q} $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
elab |
z e. {x | p} <-> [z / x] p |
| 2 |
|
elab |
z e. {y | q} <-> [z / y] q |
| 3 |
|
hyp h1 |
F/ y p |
| 4 |
|
hyp h2 |
F/ x q |
| 5 |
|
hyp e |
x = y -> (p <-> q) |
| 6 |
3, 4, 5 |
cbvsbh |
[z / x] p <-> [z / y] q |
| 7 |
1, 2, 6 |
bitr4gi |
z e. {x | p} <-> z e. {y | q} |
| 8 |
7 |
eqri |
{x | p} == {y | q} |
Axiom use
axs_prop_calc
(ax_1,
ax_2,
ax_3,
ax_mp),
axs_pred_calc
(ax_gen,
ax_4,
ax_5,
ax_6,
ax_7,
ax_10,
ax_11,
ax_12),
axs_set
(elab)