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Mirrors > Home > ILE Home > Th. List > acexmidlem1 | Unicode version |
Description: Lemma for acexmid 5741. List the cases identified in acexmidlemcase 5737 and hook them up to the lemmas which handle each case. (Contributed by Jim Kingdon, 7-Aug-2019.) |
Ref | Expression |
---|---|
acexmidlem.a | |
acexmidlem.b | |
acexmidlem.c |
Ref | Expression |
---|---|
acexmidlem1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | acexmidlem.a | . . 3 | |
2 | acexmidlem.b | . . 3 | |
3 | acexmidlem.c | . . 3 | |
4 | 1, 2, 3 | acexmidlemcase 5737 | . 2 |
5 | 1, 2, 3 | acexmidlema 5733 | . . . 4 |
6 | 5 | orcd 707 | . . 3 |
7 | 1, 2, 3 | acexmidlemb 5734 | . . . 4 |
8 | 7 | orcd 707 | . . 3 |
9 | 1, 2, 3 | acexmidlemab 5736 | . . . 4 |
10 | 9 | olcd 708 | . . 3 |
11 | 6, 8, 10 | 3jaoi 1266 | . 2 |
12 | 4, 11 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wo 682 w3o 946 wceq 1316 wcel 1465 wral 2393 wrex 2394 wreu 2395 crab 2397 c0 3333 csn 3497 cpr 3498 crio 5697 |
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-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-nul 4024 ax-pow 4068 |
This theorem depends on definitions: df-bi 116 df-3or 948 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-reu 2400 df-rab 2402 df-v 2662 df-sbc 2883 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-uni 3707 df-tr 3997 df-iord 4258 df-on 4260 df-suc 4263 df-iota 5058 df-riota 5698 |
This theorem is referenced by: acexmidlem2 5739 |
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