theorem rnrlam (a: nat) {x: nat} (b: nat x):
$ Ran (\. x e. a, b) == (\ x, b) '' a $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqstr |
Ran (\. x e. a, b) == Ran ((\ x, b) |` a) -> Ran ((\ x, b) |` a) == (\ x, b) '' a -> Ran (\. x e. a, b) == (\ x, b) '' a |
| 2 |
|
rneq |
\. x e. a, b == (\ x, b) |` a -> Ran (\. x e. a, b) == Ran ((\ x, b) |` a) |
| 3 |
|
rlameqs |
\. x e. a, b == (\ x, b) |` a |
| 4 |
2, 3 |
ax_mp |
Ran (\. x e. a, b) == Ran ((\ x, b) |` a) |
| 5 |
1, 4 |
ax_mp |
Ran ((\ x, b) |` a) == (\ x, b) '' a -> Ran (\. x e. a, b) == (\ x, b) '' a |
| 6 |
|
rnres |
Ran ((\ x, b) |` a) == (\ x, b) '' a |
| 7 |
5, 6 |
ax_mp |
Ran (\. x e. a, b) == (\ x, b) '' a |
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)