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Mirrors > Home > ILE Home > Th. List > exmidontriimlem1 | Unicode version |
Description: Lemma for exmidontriim 7202. A variation of r19.30dc 2617. (Contributed by Jim Kingdon, 12-Aug-2024.) |
Ref | Expression |
---|---|
exmidontriimlem1 | EXMID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3orass 976 | . . . . . . . 8 | |
2 | 1 | biimpi 119 | . . . . . . 7 |
3 | 2 | orcomd 724 | . . . . . 6 |
4 | 3 | ralimi 2533 | . . . . 5 |
5 | exmidexmid 4182 | . . . . 5 EXMID DECID | |
6 | r19.30dc 2617 | . . . . 5 DECID | |
7 | 4, 5, 6 | syl2an 287 | . . . 4 EXMID |
8 | 7 | orcomd 724 | . . 3 EXMID |
9 | simpr 109 | . . . . . 6 EXMID | |
10 | simplr 525 | . . . . . 6 EXMID EXMID | |
11 | orcom 723 | . . . . . . . . . 10 | |
12 | 11 | ralbii 2476 | . . . . . . . . 9 |
13 | 12 | biimpi 119 | . . . . . . . 8 |
14 | exmidexmid 4182 | . . . . . . . 8 EXMID DECID | |
15 | r19.30dc 2617 | . . . . . . . 8 DECID | |
16 | 13, 14, 15 | syl2an 287 | . . . . . . 7 EXMID |
17 | 16 | orcomd 724 | . . . . . 6 EXMID |
18 | 9, 10, 17 | syl2anc 409 | . . . . 5 EXMID |
19 | 18 | ex 114 | . . . 4 EXMID |
20 | 19 | orim2d 783 | . . 3 EXMID |
21 | 8, 20 | mpd 13 | . 2 EXMID |
22 | 3orass 976 | . 2 | |
23 | 21, 22 | sylibr 133 | 1 EXMID |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wo 703 DECID wdc 829 w3o 972 wral 2448 wrex 2449 EXMIDwem 4180 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-sep 4107 ax-nul 4115 ax-pow 4160 |
This theorem depends on definitions: df-bi 116 df-dc 830 df-3or 974 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-rab 2457 df-v 2732 df-dif 3123 df-in 3127 df-ss 3134 df-nul 3415 df-pw 3568 df-sn 3589 df-exmid 4181 |
This theorem is referenced by: exmidontriimlem2 7199 |
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