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Mirrors > Home > ILE Home > Th. List > genpprecll | Unicode version |
Description: Pre-closure law for general operation on lower cuts. (Contributed by Jim Kingdon, 2-Oct-2019.) |
Ref | Expression |
---|---|
genpelvl.1 | |
genpelvl.2 |
Ref | Expression |
---|---|
genpprecll |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2139 | . . 3 | |
2 | rspceov 5813 | . . 3 | |
3 | 1, 2 | mp3an3 1304 | . 2 |
4 | genpelvl.1 | . . 3 | |
5 | genpelvl.2 | . . 3 | |
6 | 4, 5 | genpelvl 7320 | . 2 |
7 | 3, 6 | syl5ibr 155 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 962 wceq 1331 wcel 1480 wrex 2417 crab 2420 cop 3530 cfv 5123 (class class class)co 5774 cmpo 5776 c1st 6036 c2nd 6037 cnq 7088 cnp 7099 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-coll 4043 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-un 4355 ax-setind 4452 ax-iinf 4502 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-ral 2421 df-rex 2422 df-reu 2423 df-rab 2425 df-v 2688 df-sbc 2910 df-csb 3004 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-int 3772 df-iun 3815 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-iom 4505 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-res 4551 df-ima 4552 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-f1 5128 df-fo 5129 df-f1o 5130 df-fv 5131 df-ov 5777 df-oprab 5778 df-mpo 5779 df-1st 6038 df-2nd 6039 df-qs 6435 df-ni 7112 df-nqqs 7156 df-inp 7274 |
This theorem is referenced by: genpml 7325 genprndl 7329 addnqprl 7337 mulnqprl 7376 distrlem1prl 7390 distrlem4prl 7392 ltaddpr 7405 ltexprlemrl 7418 addcanprleml 7422 addcanprlemu 7423 |
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