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Mirrors > Home > ILE Home > Th. List > recexprlemlol | Unicode version |
Description: The lower cut of is lower. Lemma for recexpr 7553. (Contributed by Jim Kingdon, 28-Dec-2019.) |
Ref | Expression |
---|---|
recexpr.1 |
Ref | Expression |
---|---|
recexprlemlol |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltsonq 7313 | . . . . . . . . 9 | |
2 | ltrelnq 7280 | . . . . . . . . 9 | |
3 | 1, 2 | sotri 4980 | . . . . . . . 8 |
4 | 3 | ex 114 | . . . . . . 7 |
5 | 4 | anim1d 334 | . . . . . 6 |
6 | 5 | eximdv 1860 | . . . . 5 |
7 | recexpr.1 | . . . . . 6 | |
8 | 7 | recexprlemell 7537 | . . . . 5 |
9 | 7 | recexprlemell 7537 | . . . . 5 |
10 | 6, 8, 9 | 3imtr4g 204 | . . . 4 |
11 | 10 | imp 123 | . . 3 |
12 | 11 | rexlimivw 2570 | . 2 |
13 | 12 | a1i 9 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wex 1472 wcel 2128 cab 2143 wrex 2436 cop 3563 class class class wbr 3965 cfv 5169 c1st 6083 c2nd 6084 cnq 7195 crq 7199 cltq 7200 cnp 7206 |
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 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-13 2130 ax-14 2131 ax-ext 2139 ax-coll 4079 ax-sep 4082 ax-nul 4090 ax-pow 4135 ax-pr 4169 ax-un 4393 ax-setind 4495 ax-iinf 4546 |
This theorem depends on definitions: df-bi 116 df-dc 821 df-3or 964 df-3an 965 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ne 2328 df-ral 2440 df-rex 2441 df-reu 2442 df-rab 2444 df-v 2714 df-sbc 2938 df-csb 3032 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3395 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-int 3808 df-iun 3851 df-br 3966 df-opab 4026 df-mpt 4027 df-tr 4063 df-eprel 4249 df-id 4253 df-po 4256 df-iso 4257 df-iord 4326 df-on 4328 df-suc 4331 df-iom 4549 df-xp 4591 df-rel 4592 df-cnv 4593 df-co 4594 df-dm 4595 df-rn 4596 df-res 4597 df-ima 4598 df-iota 5134 df-fun 5171 df-fn 5172 df-f 5173 df-f1 5174 df-fo 5175 df-f1o 5176 df-fv 5177 df-ov 5824 df-oprab 5825 df-mpo 5826 df-1st 6085 df-2nd 6086 df-recs 6249 df-irdg 6314 df-oadd 6364 df-omul 6365 df-er 6477 df-ec 6479 df-qs 6483 df-ni 7219 df-mi 7221 df-lti 7222 df-enq 7262 df-nqqs 7263 df-ltnqqs 7268 |
This theorem is referenced by: recexprlemrnd 7544 |
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