Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∈ wcel 2107
-cneg 11387 ℤcz 12500 |
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-riota 7314 df-ov 7361 df-oprab 7362 df-mpo 7363 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-sub 11388 df-neg 11389 df-nn 12155 df-z 12501 |
This theorem is referenced by: znnn0nn
12615 zriotaneg
12617 zsupss
12863 ceicl
13747 modnegd
13832 expaddzlem
14012 climshft2
15465 fsumshftm
15667 eftlub
15992 dvdsadd2b
16189 bitscmp
16319 bitsf1
16327 bitsres
16354 modgcd
16414 pcneg
16747 gznegcl
16808 gzcjcl
16809 4sqlem10
16820 mulgdirlem
18908 mulgdir
18909 mulgmodid
18916 subgmulg
18943 zringlpirlem3
20888 aannenlem1
25691 geolim3
25702 aaliou3lem1
25705 aaliou3lem2
25706 aaliou3lem3
25707 aaliou3lem5
25710 aaliou3lem6
25711 aaliou3lem7
25712 ulmshft
25752 sineq0
25883 wilthlem1
26420 lgseisenlem2
26727 2sqlem4
26772 padicabvcxp
26983 numdenneg
31716 archirngz
32028 archiabllem1b
32031 archiabllem2c
32034 mdetlap
32416 qqhval2lem
32565 breprexplemc
33248 knoppndvlem1
34978 knoppndvlem2
34979 knoppndvlem7
34984 knoppndvlem14
34991 knoppndvlem16
34993 knoppndvlem17
34994 knoppndvlem19
34996 knoppndvlem21
34998 ltflcei
36069 cntotbnd
36258 pellexlem5
41159 pell1234qrreccl
41180 pellfund14
41224 congsub
41297 acongeq
41310 dvdsacongtr
41311 jm2.19
41320 jm2.25
41326 jm2.26lem3
41328 dvradcnv2
42634 binomcxplemnotnn0
42643 sineq0ALT
43226 fourierdlem41
44396 fourierdlem48
44402 fourierdlem49
44403 fourierdlem64
44418 fourierdlem89
44443 fourierdlem91
44445 fourierdlem97
44451 fourierdlem103
44457 etransclem9
44491 etransclem35
44517 etransclem41
44523 etransclem47
44529 |