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Mirrors > Home > ILE Home > Th. List > acexmidlem1 | Unicode version |
Description: Lemma for acexmid 5773. List the cases identified in acexmidlemcase 5769 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 5769 | . 2 |
5 | 1, 2, 3 | acexmidlema 5765 | . . . 4 |
6 | 5 | orcd 722 | . . 3 |
7 | 1, 2, 3 | acexmidlemb 5766 | . . . 4 |
8 | 7 | orcd 722 | . . 3 |
9 | 1, 2, 3 | acexmidlemab 5768 | . . . 4 |
10 | 9 | olcd 723 | . . 3 |
11 | 6, 8, 10 | 3jaoi 1281 | . 2 |
12 | 4, 11 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wo 697 w3o 961 wceq 1331 wcel 1480 wral 2416 wrex 2417 wreu 2418 crab 2420 c0 3363 csn 3527 cpr 3528 crio 5729 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-nul 4054 ax-pow 4098 |
This theorem depends on definitions: df-bi 116 df-3or 963 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-reu 2423 df-rab 2425 df-v 2688 df-sbc 2910 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-nul 3364 df-pw 3512 df-sn 3533 df-pr 3534 df-uni 3737 df-tr 4027 df-iord 4288 df-on 4290 df-suc 4293 df-iota 5088 df-riota 5730 |
This theorem is referenced by: acexmidlem2 5771 |
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