theorem rlamrcl (a d: nat) {x: nat} (b c: nat x):
$ d e. (\. x e. a, b) @ c -> c e. a $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
ax_3 |
(~c e. a -> ~d e. (\. x e. a, b) @ c) -> d e. (\. x e. a, b) @ c -> c e. a |
| 2 |
|
nel0 |
~d e. 0 |
| 3 |
|
apprlam0 |
~c e. a -> (\. x e. a, b) @ c = 0 |
| 4 |
3 |
elneq2d |
~c e. a -> (d e. (\. x e. a, b) @ c <-> d e. 0) |
| 5 |
4 |
noteqd |
~c e. a -> (~d e. (\. x e. a, b) @ c <-> ~d e. 0) |
| 6 |
2, 5 |
mpbiri |
~c e. a -> ~d e. (\. x e. a, b) @ c |
| 7 |
1, 6 |
ax_mp |
d e. (\. x e. a, b) @ c -> c e. 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)