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Mirrors > Home > ILE Home > Th. List > acexmidlem1 | Unicode version |
Description: Lemma for acexmid 5835. List the cases identified in acexmidlemcase 5831 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 5831 | . 2 |
5 | 1, 2, 3 | acexmidlema 5827 | . . . 4 |
6 | 5 | orcd 723 | . . 3 |
7 | 1, 2, 3 | acexmidlemb 5828 | . . . 4 |
8 | 7 | orcd 723 | . . 3 |
9 | 1, 2, 3 | acexmidlemab 5830 | . . . 4 |
10 | 9 | olcd 724 | . . 3 |
11 | 6, 8, 10 | 3jaoi 1292 | . 2 |
12 | 4, 11 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wo 698 w3o 966 wceq 1342 wcel 2135 wral 2442 wrex 2443 wreu 2444 crab 2446 c0 3404 csn 3570 cpr 3571 crio 5791 |
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 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-nul 4102 ax-pow 4147 |
This theorem depends on definitions: df-bi 116 df-3or 968 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-reu 2449 df-rab 2451 df-v 2723 df-sbc 2947 df-dif 3113 df-un 3115 df-in 3117 df-ss 3124 df-nul 3405 df-pw 3555 df-sn 3576 df-pr 3577 df-uni 3784 df-tr 4075 df-iord 4338 df-on 4340 df-suc 4343 df-iota 5147 df-riota 5792 |
This theorem is referenced by: acexmidlem2 5833 |
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