Theorem
elArray0
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theorem elArray0 (A: set): $ 0 e. Array A 0 $;
Step
Hyp
Ref
Expression
1
elArray02
0 e. Array A 0 <-> 0 = 0
2
eqid
0 = 0
3
1
,
2
mpbir
0 e. Array A 0
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
)