![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > eluzelre | Unicode version |
Description: A member of an upper set of integers is a real. (Contributed by Mario Carneiro, 31-Aug-2013.) |
Ref | Expression |
---|---|
eluzelre |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eluzelz 9535 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | 1 | zred 9373 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4121 ax-pow 4174 ax-pr 4209 ax-cnex 7901 ax-resscn 7902 |
This theorem depends on definitions: df-bi 117 df-3or 979 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2739 df-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4004 df-opab 4065 df-mpt 4066 df-id 4293 df-xp 4632 df-rel 4633 df-cnv 4634 df-co 4635 df-dm 4636 df-rn 4637 df-res 4638 df-ima 4639 df-iota 5178 df-fun 5218 df-fn 5219 df-f 5220 df-fv 5224 df-ov 5877 df-neg 8129 df-z 9252 df-uz 9527 |
This theorem is referenced by: eluzelcn 9537 fzouzdisj 10177 eluzgtdifelfzo 10194 rebtwn2zlemstep 10250 m1modge3gt1 10368 bernneq3 10639 hashfzp1 10799 seq3coll 10817 sumsnf 11412 infssuzex 11944 infssuzledc 11945 isprm5 12136 dfphi2 12214 pclemub 12281 pockthg 12349 logbrec 14271 logbleb 14272 logbgcd1irr 14278 |
Copyright terms: Public domain | W3C validator |