theorem nffunc {x: nat} (F A B: set x):
$ FS/ x F $ >
$ FS/ x A $ >
$ FS/ x B $ >
$ F/ x func F A B $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
hyp hF |
FS/ x F |
| 2 |
1 |
nfisf |
F/ x isfun F |
| 3 |
1 |
nfdm |
FS/ x Dom F |
| 4 |
|
hyp hA |
FS/ x A |
| 5 |
3, 4 |
nfeqs |
F/ x Dom F == A |
| 6 |
2, 5 |
nfan |
F/ x isfun F /\ Dom F == A |
| 7 |
1 |
nfrn |
FS/ x Ran F |
| 8 |
|
hyp hB |
FS/ x B |
| 9 |
7, 8 |
nfss |
F/ x Ran F C_ B |
| 10 |
6, 9 |
nfan |
F/ x isfun F /\ Dom F == A /\ Ran F C_ B |
| 11 |
10 |
conv func |
F/ x func F 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)