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Mirrors > Home > ILE Home > Th. List > onsucelsucexmidlem1 | Unicode version |
Description: Lemma for onsucelsucexmid 4415. (Contributed by Jim Kingdon, 2-Aug-2019.) |
Ref | Expression |
---|---|
onsucelsucexmidlem1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0ex 4025 | . . 3 | |
2 | 1 | prid1 3599 | . 2 |
3 | eqid 2117 | . . 3 | |
4 | 3 | orci 705 | . 2 |
5 | eqeq1 2124 | . . . 4 | |
6 | 5 | orbi1d 765 | . . 3 |
7 | 6 | elrab 2813 | . 2 |
8 | 2, 4, 7 | mpbir2an 911 | 1 |
Colors of variables: wff set class |
Syntax hints: wo 682 wceq 1316 wcel 1465 crab 2397 c0 3333 csn 3497 cpr 3498 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-nul 4024 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rab 2402 df-v 2662 df-dif 3043 df-un 3045 df-nul 3334 df-sn 3503 df-pr 3504 |
This theorem is referenced by: onsucelsucexmidlem 4414 onsucelsucexmid 4415 acexmidlem2 5739 |
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