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Mirrors > Home > ILE Home > Th. List > regexmidlemm | Unicode version |
Description: Lemma for regexmid 4493. is inhabited. (Contributed by Jim Kingdon, 3-Sep-2019.) |
Ref | Expression |
---|---|
regexmidlemm.a |
Ref | Expression |
---|---|
regexmidlemm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | p0ex 4149 | . . . 4 | |
2 | 1 | prid2 3666 | . . 3 |
3 | eqid 2157 | . . . 4 | |
4 | 3 | orci 721 | . . 3 |
5 | eqeq1 2164 | . . . . 5 | |
6 | eqeq1 2164 | . . . . . 6 | |
7 | 6 | anbi1d 461 | . . . . 5 |
8 | 5, 7 | orbi12d 783 | . . . 4 |
9 | regexmidlemm.a | . . . 4 | |
10 | 8, 9 | elrab2 2871 | . . 3 |
11 | 2, 4, 10 | mpbir2an 927 | . 2 |
12 | elex2 2728 | . 2 | |
13 | 11, 12 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wo 698 wceq 1335 wex 1472 wcel 2128 crab 2439 c0 3394 csn 3560 cpr 3561 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4082 ax-nul 4090 ax-pow 4135 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rab 2444 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3395 df-pw 3545 df-sn 3566 df-pr 3567 |
This theorem is referenced by: regexmid 4493 reg2exmid 4494 reg3exmid 4538 nnregexmid 4579 |
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