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Mirrors > Home > ILE Home > Th. List > acexmidlemab | Unicode version |
Description: Lemma for acexmid 5741. (Contributed by Jim Kingdon, 6-Aug-2019.) |
Ref | Expression |
---|---|
acexmidlem.a | |
acexmidlem.b | |
acexmidlem.c |
Ref | Expression |
---|---|
acexmidlemab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3337 | . . . 4 | |
2 | 0ex 4025 | . . . . . 6 | |
3 | 2 | snid 3526 | . . . . 5 |
4 | eleq2 2181 | . . . . 5 | |
5 | 3, 4 | mpbiri 167 | . . . 4 |
6 | 1, 5 | mto 636 | . . 3 |
7 | acexmidlem.a | . . . . . . . . . 10 | |
8 | acexmidlem.b | . . . . . . . . . 10 | |
9 | acexmidlem.c | . . . . . . . . . 10 | |
10 | 7, 8, 9 | acexmidlemph 5735 | . . . . . . . . 9 |
11 | id 19 | . . . . . . . . . 10 | |
12 | eleq1 2180 | . . . . . . . . . . . 12 | |
13 | 12 | anbi1d 460 | . . . . . . . . . . 11 |
14 | 13 | rexbidv 2415 | . . . . . . . . . 10 |
15 | 11, 14 | riotaeqbidv 5701 | . . . . . . . . 9 |
16 | 10, 15 | syl 14 | . . . . . . . 8 |
17 | 16 | eqeq1d 2126 | . . . . . . 7 |
18 | 17 | biimpa 294 | . . . . . 6 |
19 | 18 | adantrr 470 | . . . . 5 |
20 | simprr 506 | . . . . 5 | |
21 | 19, 20 | eqtr3d 2152 | . . . 4 |
22 | 21 | ex 114 | . . 3 |
23 | 6, 22 | mtoi 638 | . 2 |
24 | 23 | con2i 601 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wo 682 wceq 1316 wcel 1465 wrex 2394 crab 2397 c0 3333 csn 3497 cpr 3498 crio 5697 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-nul 4024 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-dif 3043 df-nul 3334 df-sn 3503 df-uni 3707 df-iota 5058 df-riota 5698 |
This theorem is referenced by: acexmidlem1 5738 |
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