theorem eelabd (G: wff) {x: nat} (a: nat x) (p: wff x) (q: wff):
$ G -> p -> q $ >
$ G -> a e. {x | p} -> q $;
| Step | Hyp | Ref | Expression |
|---|
| 1 |
|
eleq1 |
y = a -> (y e. {x | p} <-> a e. {x | p}) |
| 2 |
1 |
iexe |
a e. {x | p} -> E. y y e. {x | p} |
| 3 |
|
hyp h |
G -> p -> q |
| 4 |
3 |
anwl |
G /\ x = y -> p -> q |
| 5 |
4 |
ssabed |
G -> y e. {x | p} -> q |
| 6 |
5 |
eexd |
G -> E. y y e. {x | p} -> q |
| 7 |
2, 6 |
syl5 |
G -> a e. {x | p} -> q |
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)