theorem elxabe (A: set) (a b: nat) (p: wff) {x: nat} (B: set x):
$ x = a -> (b e. B <-> p) $ >
$ a, b e. X\ x e. A, B <-> a e. A /\ p $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
hyp h |
x = a -> (b e. B <-> p) |
| 2 |
1 |
anwr |
T. /\ x = a -> (b e. B <-> p) |
| 3 |
2 |
elxabed |
T. -> (a, b e. X\ x e. A, B <-> a e. A /\ p) |
| 4 |
3 |
trud |
a, b e. X\ x e. A, B <-> a e. A /\ p |
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),
axs_the
(theid,
the0),
axs_peano
(peano1,
peano2,
peano5,
addeq,
muleq,
add0,
addS,
mul0,
mulS)