theorem nfxab {x y: nat} (A B: set x y):
$ FS/ y A $ >
$ FS/ y B $ >
$ FS/ y X\ x e. A, B $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
hyp h1 |
FS/ y A |
| 2 |
1 |
nfel2 |
F/ y fst a1 e. A |
| 3 |
|
hyp h2 |
FS/ y B |
| 4 |
3 |
nfsbs |
FS/ y S[fst a1 / x] B |
| 5 |
4 |
nfel2 |
F/ y snd a1 e. S[fst a1 / x] B |
| 6 |
2, 5 |
nfan |
F/ y fst a1 e. A /\ snd a1 e. S[fst a1 / x] B |
| 7 |
6 |
nfab |
FS/ y {a1 | fst a1 e. A /\ snd a1 e. S[fst a1 / x] B} |
| 8 |
7 |
conv xab |
FS/ y X\ x e. A, B |
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)