theorem eqlower2 (A: set) (a: nat): $ finite A -> (a == A <-> a = lower A) $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eqscomb |
a == A <-> A == a |
| 2 |
|
eqcomb |
a = lower A <-> lower A = a |
| 3 |
|
eqlower1 |
finite A -> (A == a <-> lower A = a) |
| 4 |
1, 2, 3 |
bitr4g |
finite A -> (a == A <-> a = lower 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)