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Mirrors > Home > ILE Home > Th. List > acexmidlem1 | Unicode version |
Description: Lemma for acexmid 5511. List the cases identified in acexmidlemcase 5507 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 5507 | . 2 |
5 | 1, 2, 3 | acexmidlema 5503 | . . . 4 |
6 | 5 | orcd 652 | . . 3 |
7 | 1, 2, 3 | acexmidlemb 5504 | . . . 4 |
8 | 7 | orcd 652 | . . 3 |
9 | 1, 2, 3 | acexmidlemab 5506 | . . . 4 |
10 | 9 | olcd 653 | . . 3 |
11 | 6, 8, 10 | 3jaoi 1198 | . 2 |
12 | 4, 11 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wo 629 w3o 884 wceq 1243 wcel 1393 wral 2306 wrex 2307 wreu 2308 crab 2310 c0 3224 csn 3375 cpr 3376 crio 5467 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-nul 3883 ax-pow 3927 |
This theorem depends on definitions: df-bi 110 df-3or 886 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-reu 2313 df-rab 2315 df-v 2559 df-sbc 2765 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-nul 3225 df-pw 3361 df-sn 3381 df-pr 3382 df-uni 3581 df-tr 3855 df-iord 4103 df-on 4105 df-suc 4108 df-iota 4867 df-riota 5468 |
This theorem is referenced by: acexmidlem2 5509 |
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