Colors of
variables: wff
setvar class |
Syntax hints:
∈ wcel 2107 ∀wral 3062
⊆ wss 3949 (class class class)co 7409
ℝcr 11109 1c1 11111
+ caddc 11113 ℕcn 12212 |
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 5300 ax-nul 5307 ax-pr 5428 ax-un 7725 ax-1cn 11168 ax-icn 11169 ax-addcl 11170 ax-addrcl 11171 ax-mulcl 11172 ax-mulrcl 11173 ax-i2m1 11178 ax-1ne0 11179 ax-rrecex 11182 ax-cnre 11183 |
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 2942 df-ral 3063 df-rex 3072 df-reu 3378 df-rab 3434 df-v 3477 df-sbc 3779 df-csb 3895 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-pss 3968 df-nul 4324 df-if 4530 df-pw 4605 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4910 df-iun 5000 df-br 5150 df-opab 5212 df-mpt 5233 df-tr 5267 df-id 5575 df-eprel 5581 df-po 5589 df-so 5590 df-fr 5632 df-we 5634 df-xp 5683 df-rel 5684 df-cnv 5685 df-co 5686 df-dm 5687 df-rn 5688 df-res 5689 df-ima 5690 df-pred 6301 df-ord 6368 df-on 6369 df-lim 6370 df-suc 6371 df-iota 6496 df-fun 6546 df-fn 6547 df-f 6548 df-f1 6549 df-fo 6550 df-f1o 6551 df-fv 6552 df-ov 7412 df-om 7856 df-2nd 7976 df-frecs 8266 df-wrecs 8297 df-recs 8371 df-rdg 8410 df-nn 12213 |
This theorem is referenced by: nnre
12219 dfnn3
12226 nnred
12227 nnunb
12468 nn0ssre
12476 isercolllem1
15611 isercolllem2
15612 isercoll
15614 o1fsum
15759 ruc
16186 prmgaplem3
16986 prmgaplem4
16987 gsumval3
19775 ovolctb2
25009 ovolicc2lem3
25036 ovolicc2lem4
25037 iundisj2
25066 iundisj2f
31821 ssnnssfz
31998 iundisjfi
32007 iundisj2fi
32008 xrsmulgzz
32179 ballotlemsup
33503 reprlt
33631 reprgt
33633 erdszelem5
34186 erdszelem7
34188 erdszelem8
34189 incsequz2
36617 sticksstones1
40962 stoweidlem34
44750 fourierdlem31
44854 prmdvdsfmtnof1lem1
46252 prmdvdsfmtnof
46254 |