Colors of
variables: wff
setvar class |
Syntax hints:
∈ wcel 2107 ∀wral 3061
⊆ wss 3914 (class class class)co 7361
ℝcr 11058 1c1 11060
+ caddc 11062 ℕcn 12161 |
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 2704 ax-sep 5260 ax-nul 5267 ax-pr 5388 ax-un 7676 ax-1cn 11117 ax-icn 11118 ax-addcl 11119 ax-addrcl 11120 ax-mulcl 11121 ax-mulrcl 11122 ax-i2m1 11127 ax-1ne0 11128 ax-rrecex 11131 ax-cnre 11132 |
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 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2941 df-ral 3062 df-rex 3071 df-reu 3353 df-rab 3407 df-v 3449 df-sbc 3744 df-csb 3860 df-dif 3917 df-un 3919 df-in 3921 df-ss 3931 df-pss 3933 df-nul 4287 df-if 4491 df-pw 4566 df-sn 4591 df-pr 4593 df-op 4597 df-uni 4870 df-iun 4960 df-br 5110 df-opab 5172 df-mpt 5193 df-tr 5227 df-id 5535 df-eprel 5541 df-po 5549 df-so 5550 df-fr 5592 df-we 5594 df-xp 5643 df-rel 5644 df-cnv 5645 df-co 5646 df-dm 5647 df-rn 5648 df-res 5649 df-ima 5650 df-pred 6257 df-ord 6324 df-on 6325 df-lim 6326 df-suc 6327 df-iota 6452 df-fun 6502 df-fn 6503 df-f 6504 df-f1 6505 df-fo 6506 df-f1o 6507 df-fv 6508 df-ov 7364 df-om 7807 df-2nd 7926 df-frecs 8216 df-wrecs 8247 df-recs 8321 df-rdg 8360 df-nn 12162 |
This theorem is referenced by: nnre
12168 dfnn3
12175 nnred
12176 nnunb
12417 nn0ssre
12425 isercolllem1
15558 isercolllem2
15559 isercoll
15561 o1fsum
15706 ruc
16133 prmgaplem3
16933 prmgaplem4
16934 gsumval3
19692 ovolctb2
24879 ovolicc2lem3
24906 ovolicc2lem4
24907 iundisj2
24936 iundisj2f
31561 ssnnssfz
31744 iundisjfi
31753 iundisj2fi
31754 xrsmulgzz
31925 ballotlemsup
33168 reprlt
33296 reprgt
33298 erdszelem5
33853 erdszelem7
33855 erdszelem8
33856 incsequz2
36258 sticksstones1
40604 stoweidlem34
44365 fourierdlem31
44469 prmdvdsfmtnof1lem1
45866 prmdvdsfmtnof
45868 |