Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ w3a 1086
∈ wcel 2105 class class class wbr 5092
‘cfv 6479 (class class class)co 7337
≤ cle 11111 −
cmin 11306 ℕ0cn0 12334 ℤcz 12420 ℤ≥cuz 12683 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912
ax-6 1970 ax-7 2010 ax-8 2107
ax-9 2115 ax-10 2136 ax-11 2153 ax-12 2170 ax-ext 2707 ax-sep 5243 ax-nul 5250 ax-pow 5308 ax-pr 5372 ax-un 7650 ax-cnex 11028 ax-resscn 11029 ax-1cn 11030 ax-icn 11031 ax-addcl 11032 ax-addrcl 11033 ax-mulcl 11034 ax-mulrcl 11035 ax-mulcom 11036 ax-addass 11037 ax-mulass 11038 ax-distr 11039 ax-i2m1 11040 ax-1ne0 11041 ax-1rid 11042 ax-rnegex 11043 ax-rrecex 11044 ax-cnre 11045 ax-pre-lttri 11046 ax-pre-lttrn 11047 ax-pre-ltadd 11048 ax-pre-mulgt0 11049 |
This theorem depends on definitions:
df-bi 206 df-an 397
df-or 845 df-3or 1087 df-3an 1088 df-tru 1543 df-fal 1553 df-ex 1781 df-nf 1785 df-sb 2067 df-mo 2538 df-eu 2567 df-clab 2714 df-cleq 2728 df-clel 2814 df-nfc 2886 df-ne 2941 df-nel 3047 df-ral 3062 df-rex 3071 df-reu 3350 df-rab 3404 df-v 3443 df-sbc 3728 df-csb 3844 df-dif 3901 df-un 3903 df-in 3905 df-ss 3915 df-pss 3917 df-nul 4270 df-if 4474 df-pw 4549 df-sn 4574 df-pr 4576 df-op 4580 df-uni 4853 df-iun 4943 df-br 5093 df-opab 5155 df-mpt 5176 df-tr 5210 df-id 5518 df-eprel 5524 df-po 5532 df-so 5533 df-fr 5575 df-we 5577 df-xp 5626 df-rel 5627 df-cnv 5628 df-co 5629 df-dm 5630 df-rn 5631 df-res 5632 df-ima 5633 df-pred 6238 df-ord 6305 df-on 6306 df-lim 6307 df-suc 6308 df-iota 6431 df-fun 6481 df-fn 6482 df-f 6483 df-f1 6484 df-fo 6485 df-f1o 6486 df-fv 6487 df-riota 7293 df-ov 7340 df-oprab 7341 df-mpo 7342 df-om 7781 df-2nd 7900 df-frecs 8167 df-wrecs 8198 df-recs 8272 df-rdg 8311 df-er 8569 df-en 8805 df-dom 8806 df-sdom 8807 df-pnf 11112 df-mnf 11113 df-xr 11114 df-ltxr 11115 df-le 11116 df-sub 11308 df-neg 11309 df-nn 12075 df-n0 12335 df-z 12421
df-uz 12684 |
This theorem is referenced by: fznn0sub
13389 elfzmlbm
13467 fzen2
13790 fzfi
13793 leexp2a
13991 hashfz
14242 ccatrn
14393 swrds2m
14753 isercoll2
15479 iseralt
15495 cvgrat
15694 fprodser
15758 dvdsexp
16136 bitsshft
16281 prmm2nn0
16500 hashdvds
16573 prmdiv
16583 prmdiveq
16584 pcaddlem
16686 vdwlem5
16783 vdwlem8
16786 dvn2bss
25200 aaliou3lem2
25609 lgsquadlem1
26634 crctcshwlkn0lem5
28467 clwwlknonex2lem1
28759 clwwlknonex2lem2
28760 numclwlk1lem2
29022 numclwwlk3lem1
29034 fiblem
32665 signstfveq0
32856 irrapxlem3
40908 itgsinexp
43832 wallispilem3
43944 fmtnorec3
45351 fmtnorec4
45352 |