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Mirrors > Home > ILE Home > Th. List > exmidontriimlem1 | Unicode version |
Description: Lemma for exmidontriim 7161. A variation of r19.30dc 2604. (Contributed by Jim Kingdon, 12-Aug-2024.) |
Ref | Expression |
---|---|
exmidontriimlem1 | EXMID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3orass 966 | . . . . . . . 8 | |
2 | 1 | biimpi 119 | . . . . . . 7 |
3 | 2 | orcomd 719 | . . . . . 6 |
4 | 3 | ralimi 2520 | . . . . 5 |
5 | exmidexmid 4158 | . . . . 5 EXMID DECID | |
6 | r19.30dc 2604 | . . . . 5 DECID | |
7 | 4, 5, 6 | syl2an 287 | . . . 4 EXMID |
8 | 7 | orcomd 719 | . . 3 EXMID |
9 | simpr 109 | . . . . . 6 EXMID | |
10 | simplr 520 | . . . . . 6 EXMID EXMID | |
11 | orcom 718 | . . . . . . . . . 10 | |
12 | 11 | ralbii 2463 | . . . . . . . . 9 |
13 | 12 | biimpi 119 | . . . . . . . 8 |
14 | exmidexmid 4158 | . . . . . . . 8 EXMID DECID | |
15 | r19.30dc 2604 | . . . . . . . 8 DECID | |
16 | 13, 14, 15 | syl2an 287 | . . . . . . 7 EXMID |
17 | 16 | orcomd 719 | . . . . . 6 EXMID |
18 | 9, 10, 17 | syl2anc 409 | . . . . 5 EXMID |
19 | 18 | ex 114 | . . . 4 EXMID |
20 | 19 | orim2d 778 | . . 3 EXMID |
21 | 8, 20 | mpd 13 | . 2 EXMID |
22 | 3orass 966 | . 2 | |
23 | 21, 22 | sylibr 133 | 1 EXMID |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wo 698 DECID wdc 820 w3o 962 wral 2435 wrex 2436 EXMIDwem 4156 |
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-14 2131 ax-ext 2139 ax-sep 4083 ax-nul 4091 ax-pow 4136 |
This theorem depends on definitions: df-bi 116 df-dc 821 df-3or 964 df-tru 1338 df-fal 1341 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-rab 2444 df-v 2714 df-dif 3104 df-in 3108 df-ss 3115 df-nul 3395 df-pw 3545 df-sn 3566 df-exmid 4157 |
This theorem is referenced by: exmidontriimlem2 7158 |
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