theorem eqapp (F G: set) (a: nat) {y: nat}:
$ A. y (a, y e. F <-> a, y e. G) -> F @ a = G @ a $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
abeq |
A. y (a, y e. F <-> a, y e. G) -> {y | a, y e. F} == {y | a, y e. G} |
| 2 |
1 |
theeqd |
A. y (a, y e. F <-> a, y e. G) -> the {y | a, y e. F} = the {y | a, y e. G} |
| 3 |
2 |
conv app |
A. y (a, y e. F <-> a, y e. G) -> F @ a = G @ 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)