theorem splitpr2 (G: wff) (a b: nat) (p: wff) (x y: nat):
$ G -> a = x, y -> p $ >
$ G -> b = y -> a = x, b -> p $;
Step | Hyp | Ref | Expression |
1 |
|
hyp h |
G -> a = x, y -> p |
2 |
|
anll |
G /\ b = y /\ a = x, b -> G |
3 |
|
anr |
G /\ b = y /\ a = x, b -> a = x, b |
4 |
|
anlr |
G /\ b = y /\ a = x, b -> b = y |
5 |
4 |
preq2d |
G /\ b = y /\ a = x, b -> x, b = x, y |
6 |
3, 5 |
eqtrd |
G /\ b = y /\ a = x, b -> a = x, y |
7 |
1, 2, 6 |
sylc |
G /\ b = y /\ a = x, b -> p |
8 |
7 |
exp |
G /\ b = y -> a = x, b -> p |
9 |
8 |
exp |
G -> b = y -> a = x, b -> p |
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
(peano2,
addeq,
muleq)