Colors of
variables: wff
setvar class |
Syntax hints:
∈ wcel 2106 ∀wral 3061
⊆ wss 3948 (class class class)co 7408
ℝcr 11108 1c1 11110
+ caddc 11112 ℕcn 12211 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913
ax-6 1971 ax-7 2011 ax-8 2108
ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2703 ax-sep 5299 ax-nul 5306 ax-pr 5427 ax-un 7724 ax-1cn 11167 ax-icn 11168 ax-addcl 11169 ax-addrcl 11170 ax-mulcl 11171 ax-mulrcl 11172 ax-i2m1 11177 ax-1ne0 11178 ax-rrecex 11181 ax-cnre 11182 |
This theorem depends on definitions:
df-bi 206 df-an 397
df-or 846 df-3or 1088 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2534 df-eu 2563 df-clab 2710 df-cleq 2724 df-clel 2810 df-nfc 2885 df-ne 2941 df-ral 3062 df-rex 3071 df-reu 3377 df-rab 3433 df-v 3476 df-sbc 3778 df-csb 3894 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-pss 3967 df-nul 4323 df-if 4529 df-pw 4604 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-iun 4999 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5574 df-eprel 5580 df-po 5588 df-so 5589 df-fr 5631 df-we 5633 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-rn 5687 df-res 5688 df-ima 5689 df-pred 6300 df-ord 6367 df-on 6368 df-lim 6369 df-suc 6370 df-iota 6495 df-fun 6545 df-fn 6546 df-f 6547 df-f1 6548 df-fo 6549 df-f1o 6550 df-fv 6551 df-ov 7411 df-om 7855 df-2nd 7975 df-frecs 8265 df-wrecs 8296 df-recs 8370 df-rdg 8409 df-nn 12212 |
This theorem is referenced by: nnre
12218 dfnn3
12225 nnred
12226 nnunb
12467 nn0ssre
12475 isercolllem1
15610 isercolllem2
15611 isercoll
15613 o1fsum
15758 ruc
16185 prmgaplem3
16985 prmgaplem4
16986 gsumval3
19774 ovolctb2
25008 ovolicc2lem3
25035 ovolicc2lem4
25036 iundisj2
25065 iundisj2f
31816 ssnnssfz
31993 iundisjfi
32002 iundisj2fi
32003 xrsmulgzz
32174 ballotlemsup
33498 reprlt
33626 reprgt
33628 erdszelem5
34181 erdszelem7
34183 erdszelem8
34184 incsequz2
36612 sticksstones1
40957 stoweidlem34
44740 fourierdlem31
44844 prmdvdsfmtnof1lem1
46242 prmdvdsfmtnof
46244 |