theorem rappsabed2 (B F: set) (G: wff) (a: nat) {x: nat} (A: set x):
$ G /\ x = a -> A == B $ >
$ G -> F == S\ x, A -> F @' a == B $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
hyp e |
G /\ x = a -> A == B |
| 2 |
1 |
eqseq2d |
G /\ x = a -> (F @' a == A <-> F @' a == B) |
| 3 |
2 |
bi1d |
G /\ x = a -> F @' a == A -> F @' a == B |
| 4 |
3 |
rappsabed1 |
G -> F == S\ x, A -> 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),
axs_the
(theid,
the0),
axs_peano
(peano1,
peano2,
peano5,
addeq,
muleq,
add0,
addS,
mul0,
mulS)