theorem elabed2 (A: set) (G: wff) (a: nat) (q: wff) {x: nat} (p: wff x):
$ G /\ x = a -> (p <-> q) $ >
$ G -> A == {x | p} -> (a e. A <-> q) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
hyp e |
G /\ x = a -> (p <-> q) |
| 2 |
1 |
bieq2d |
G /\ x = a -> (a e. A <-> p <-> (a e. A <-> q)) |
| 3 |
2 |
bi1d |
G /\ x = a -> (a e. A <-> p) -> (a e. A <-> q) |
| 4 |
3 |
elabed1 |
G -> A == {x | p} -> (a e. A <-> q) |
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)