Colors of
variables: wff
setvar class |
Syntax hints:
β§ w3a 1088 βwral 3065
βwrex 3074 Vcvv 3448
class class class wbr 5110 Rel wrel 5643
βΆwf 6497 βcfv 6501 (class class class)co 7362
βm cmap 8772
βcc 11056 <
clt 11196 β cmin 11392
β€cz 12506 β€β₯cuz 12770 β+crp 12922 abscabs 15126
βπ’culm 25751 |
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 |
This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 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-sbc 3745 df-csb 3861 df-dif 3918 df-un 3920 df-in 3922 df-ss 3932 df-nul 4288 df-if 4492 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-fv 6509 df-ulm 25752 |
This theorem is referenced by: ulmval
25755 ulmdm
25768 ulmcau
25770 ulmdvlem3
25777 |