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Mirrors > Home > ILE Home > Th. List > ivthinclemum | Unicode version |
Description: Lemma for ivthinc 13188. The upper cut is bounded. (Contributed by Jim Kingdon, 18-Feb-2024.) |
Ref | Expression |
---|---|
ivth.1 | |
ivth.2 | |
ivth.3 | |
ivth.4 | |
ivth.5 | |
ivth.7 | |
ivth.8 | |
ivth.9 | |
ivthinc.i | |
ivthinclem.l | |
ivthinclem.r |
Ref | Expression |
---|---|
ivthinclemum |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ivth.1 | . . . 4 | |
2 | 1 | rexrd 7940 | . . 3 |
3 | ivth.2 | . . . 4 | |
4 | 3 | rexrd 7940 | . . 3 |
5 | ivth.4 | . . . 4 | |
6 | 1, 3, 5 | ltled 8009 | . . 3 |
7 | ubicc2 9913 | . . 3 | |
8 | 2, 4, 6, 7 | syl3anc 1227 | . 2 |
9 | ivth.9 | . . . 4 | |
10 | 9 | simprd 113 | . . 3 |
11 | fveq2 5481 | . . . . 5 | |
12 | 11 | breq2d 3989 | . . . 4 |
13 | ivthinclem.r | . . . 4 | |
14 | 12, 13 | elrab2 2881 | . . 3 |
15 | 8, 10, 14 | sylanbrc 414 | . 2 |
16 | eleq1 2227 | . . 3 | |
17 | 16 | rspcev 2826 | . 2 |
18 | 8, 15, 17 | syl2anc 409 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 wcel 2135 wrex 2443 crab 2446 wss 3112 class class class wbr 3977 cfv 5183 (class class class)co 5837 cc 7743 cr 7744 cxr 7924 clt 7925 cle 7926 cicc 9819 ccncf 13124 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4095 ax-pow 4148 ax-pr 4182 ax-un 4406 ax-setind 4509 ax-cnex 7836 ax-resscn 7837 ax-pre-ltirr 7857 ax-pre-lttrn 7859 |
This theorem depends on definitions: df-bi 116 df-3or 968 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-nel 2430 df-ral 2447 df-rex 2448 df-rab 2451 df-v 2724 df-sbc 2948 df-dif 3114 df-un 3116 df-in 3118 df-ss 3125 df-pw 3556 df-sn 3577 df-pr 3578 df-op 3580 df-uni 3785 df-br 3978 df-opab 4039 df-id 4266 df-xp 4605 df-rel 4606 df-cnv 4607 df-co 4608 df-dm 4609 df-iota 5148 df-fun 5185 df-fv 5191 df-ov 5840 df-oprab 5841 df-mpo 5842 df-pnf 7927 df-mnf 7928 df-xr 7929 df-ltxr 7930 df-le 7931 df-icc 9823 |
This theorem is referenced by: ivthinclemex 13187 |
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