Colors of
variables: wff
setvar class |
Syntax hints:
∈ wcel 2107 ∀wral 3065
{crab 3410 Vcvv 3448
𝒫 cpw 4565 class class class wbr 5110
⟶wf 6497 ≤
cle 11197 ℤcz 12506
ℤ≥cuz 12770 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914
ax-6 1972 ax-7 2012 ax-8 2109
ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2708 ax-sep 5261 ax-nul 5268 ax-pr 5389 ax-cnex 11114 ax-resscn 11115 |
This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 df-3or 1089 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2539 df-eu 2568 df-clab 2715 df-cleq 2729 df-clel 2815 df-nfc 2890 df-ral 3066 df-rex 3075 df-rab 3411 df-v 3450 df-dif 3918 df-un 3920 df-in 3922 df-ss 3932 df-nul 4288 df-if 4492 df-pw 4567 df-sn 4592 df-pr 4594 df-op 4598 df-uni 4871 df-br 5111 df-opab 5173 df-mpt 5194 df-id 5536 df-xp 5644 df-rel 5645 df-cnv 5646 df-co 5647 df-dm 5648 df-rn 5649 df-res 5650 df-ima 5651 df-iota 6453 df-fun 6503 df-fn 6504 df-f 6505 df-fv 6509 df-ov 7365 df-neg 11395 df-z 12507
df-uz 12771 |
This theorem is referenced by: eluzel2
12775 uzn0
12787 uzssz
12791 ltweuz
13873 uzin2
15236 rexanuz
15237 sumz
15614 sumss
15616 prod1
15834 prodss
15837 lmbr2
22626 lmff
22668 zfbas
23263 uzrest
23264 lmflf
23372 lmmbr2
24639 caucfil
24663 lmcau
24693 heibor1lem
36297 dmuz
43533 |