theorem ocasepeq (_z1 _z2: wff) (_S1 _S2: set):
$ (_z1 <-> _z2) -> _S1 == _S2 -> ocasep _z1 _S1 == ocasep _z2 _S2 $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
anl |
(_z1 <-> _z2) /\ _S1 == _S2 -> (_z1 <-> _z2) |
| 2 |
|
anr |
(_z1 <-> _z2) /\ _S1 == _S2 -> _S1 == _S2 |
| 3 |
1, 2 |
ocasepeqd |
(_z1 <-> _z2) /\ _S1 == _S2 -> ocasep _z1 _S1 == ocasep _z2 _S2 |
| 4 |
3 |
exp |
(_z1 <-> _z2) -> _S1 == _S2 -> ocasep _z1 _S1 == ocasep _z2 _S2 |
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)