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Mirrors > Home > ILE Home > Th. List > exmidontriimlem2 | Unicode version |
Description: Lemma for exmidontriim 7202. (Contributed by Jim Kingdon, 12-Aug-2024.) |
Ref | Expression |
---|---|
exmidontriimlem2.b | |
exmidontriimlem2.em | EXMID |
exmidontriimlem2.hb |
Ref | Expression |
---|---|
exmidontriimlem2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exmidontriimlem2.b | . . . . . 6 | |
2 | 1 | ad2antrr 485 | . . . . 5 |
3 | simpr 109 | . . . . . 6 | |
4 | simplr 525 | . . . . . 6 | |
5 | 3, 4 | jca 304 | . . . . 5 |
6 | ontr1 4374 | . . . . 5 | |
7 | 2, 5, 6 | sylc 62 | . . . 4 |
8 | 7 | r19.29an 2612 | . . 3 |
9 | 8 | orcd 728 | . 2 |
10 | simpr 109 | . . . . 5 | |
11 | simplr 525 | . . . . 5 | |
12 | 10, 11 | eqeltrd 2247 | . . . 4 |
13 | 12 | r19.29an 2612 | . . 3 |
14 | 13 | orcd 728 | . 2 |
15 | simpr 109 | . . 3 | |
16 | 15 | olcd 729 | . 2 |
17 | exmidontriimlem2.hb | . . 3 | |
18 | exmidontriimlem2.em | . . 3 EXMID | |
19 | exmidontriimlem1 7198 | . . 3 EXMID | |
20 | 17, 18, 19 | syl2anc 409 | . 2 |
21 | 9, 14, 16, 20 | mpjao3dan 1302 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wo 703 w3o 972 wceq 1348 wcel 2141 wral 2448 wrex 2449 EXMIDwem 4180 con0 4348 |
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-uni 3797 df-tr 4088 df-exmid 4181 df-iord 4351 df-on 4353 |
This theorem is referenced by: exmidontriimlem3 7200 |
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