Colors of
variables: wff
setvar class |
Syntax hints:
∈ wcel 2107 0cc0 11052
1c1 11053 ℕ0cn0 12414 ;cdc 12619 |
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 5257 ax-nul 5264 ax-pow 5321 ax-pr 5385 ax-un 7673 ax-resscn 11109 ax-1cn 11110 ax-icn 11111 ax-addcl 11112 ax-addrcl 11113 ax-mulcl 11114 ax-mulrcl 11115 ax-mulcom 11116 ax-addass 11117 ax-mulass 11118 ax-distr 11119 ax-i2m1 11120 ax-1ne0 11121 ax-1rid 11122 ax-rnegex 11123 ax-rrecex 11124 ax-cnre 11125 ax-pre-lttri 11126 ax-pre-lttrn 11127 ax-pre-ltadd 11128 |
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-ne 2945 df-nel 3051 df-ral 3066 df-rex 3075 df-reu 3355 df-rab 3409 df-v 3448 df-sbc 3741 df-csb 3857 df-dif 3914 df-un 3916 df-in 3918 df-ss 3928 df-pss 3930 df-nul 4284 df-if 4488 df-pw 4563 df-sn 4588 df-pr 4590 df-op 4594 df-uni 4867 df-iun 4957 df-br 5107 df-opab 5169 df-mpt 5190 df-tr 5224 df-id 5532 df-eprel 5538 df-po 5546 df-so 5547 df-fr 5589 df-we 5591 df-xp 5640 df-rel 5641 df-cnv 5642 df-co 5643 df-dm 5644 df-rn 5645 df-res 5646 df-ima 5647 df-pred 6254 df-ord 6321 df-on 6322 df-lim 6323 df-suc 6324 df-iota 6449 df-fun 6499 df-fn 6500 df-f 6501 df-f1 6502 df-fo 6503 df-f1o 6504 df-fv 6505 df-ov 7361 df-om 7804 df-2nd 7923 df-frecs 8213 df-wrecs 8244 df-recs 8318 df-rdg 8357 df-er 8649 df-en 8885 df-dom 8886 df-sdom 8887 df-pnf 11192 df-mnf 11193 df-ltxr 11195 df-nn 12155 df-2 12217
df-3 12218 df-4 12219
df-5 12220 df-6 12221
df-7 12222 df-8 12223
df-9 12224 df-n0 12415 df-dec 12620 |
This theorem is referenced by: decnncl
12639 dec0u
12640 dec0h
12641 decsuc
12650 decle
12653 decma
12670 decmac
12671 decma2c
12672 decadd
12673 decaddc
12674 decsubi
12682 decmul1c
12684 decmul2c
12685 decmul10add
12688 9t11e99
12749 sq10
14165 dec2dvds
16936 decsplit0b
16953 decsplit1
16955 decsplit
16956 karatsuba
16957 139prm
16997 317prm
16999 1259lem1
17004 1259lem3
17006 2503lem1
17010 4001lem1
17014 4001lem3
17016 9p10ne21
29417 dfdec100
31729 dp20u
31737 dp20h
31738 dp2clq
31740 dpmul100
31756 dpmul1000
31758 dpexpp1
31767 0dp2dp
31768 dpmul
31772 dpmul4
31773 hgt750lemd
33264 hgt750lem2
33268 hgt750leme
33274 tgoldbachgnn
33275 aks4d1p1p7
40534 sqdeccom12
40806 rmydioph
41341 tgoldbach
46016 |