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Mirrors > Home > ILE Home > Th. List > acexmidlem1 | Unicode version |
Description: Lemma for acexmid 5643. List the cases identified in acexmidlemcase 5639 and hook them up to the lemmas which handle each case. (Contributed by Jim Kingdon, 7-Aug-2019.) |
Ref | Expression |
---|---|
acexmidlem.a |
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acexmidlem.b |
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acexmidlem.c |
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Ref | Expression |
---|---|
acexmidlem1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | acexmidlem.a |
. . 3
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2 | acexmidlem.b |
. . 3
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3 | acexmidlem.c |
. . 3
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4 | 1, 2, 3 | acexmidlemcase 5639 |
. 2
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5 | 1, 2, 3 | acexmidlema 5635 |
. . . 4
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6 | 5 | orcd 687 |
. . 3
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7 | 1, 2, 3 | acexmidlemb 5636 |
. . . 4
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8 | 7 | orcd 687 |
. . 3
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9 | 1, 2, 3 | acexmidlemab 5638 |
. . . 4
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10 | 9 | olcd 688 |
. . 3
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11 | 6, 8, 10 | 3jaoi 1239 |
. 2
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12 | 4, 11 | syl 14 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-sep 3955 ax-nul 3963 ax-pow 4007 |
This theorem depends on definitions: df-bi 115 df-3or 925 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-eu 1951 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ral 2364 df-rex 2365 df-reu 2366 df-rab 2368 df-v 2621 df-sbc 2841 df-dif 3001 df-un 3003 df-in 3005 df-ss 3012 df-nul 3287 df-pw 3429 df-sn 3450 df-pr 3451 df-uni 3652 df-tr 3935 df-iord 4191 df-on 4193 df-suc 4196 df-iota 4975 df-riota 5600 |
This theorem is referenced by: acexmidlem2 5641 |
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