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Mirrors > Home > ILE Home > Th. List > acexmidlemab | Unicode version |
Description: Lemma for acexmid 5511. (Contributed by Jim Kingdon, 6-Aug-2019.) |
Ref | Expression |
---|---|
acexmidlem.a | |
acexmidlem.b | |
acexmidlem.c |
Ref | Expression |
---|---|
acexmidlemab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3228 | . . . 4 | |
2 | 0ex 3884 | . . . . . 6 | |
3 | 2 | snid 3402 | . . . . 5 |
4 | eleq2 2101 | . . . . 5 | |
5 | 3, 4 | mpbiri 157 | . . . 4 |
6 | 1, 5 | mto 588 | . . 3 |
7 | acexmidlem.a | . . . . . . . . . 10 | |
8 | acexmidlem.b | . . . . . . . . . 10 | |
9 | acexmidlem.c | . . . . . . . . . 10 | |
10 | 7, 8, 9 | acexmidlemph 5505 | . . . . . . . . 9 |
11 | id 19 | . . . . . . . . . 10 | |
12 | eleq1 2100 | . . . . . . . . . . . 12 | |
13 | 12 | anbi1d 438 | . . . . . . . . . . 11 |
14 | 13 | rexbidv 2327 | . . . . . . . . . 10 |
15 | 11, 14 | riotaeqbidv 5471 | . . . . . . . . 9 |
16 | 10, 15 | syl 14 | . . . . . . . 8 |
17 | 16 | eqeq1d 2048 | . . . . . . 7 |
18 | 17 | biimpa 280 | . . . . . 6 |
19 | 18 | adantrr 448 | . . . . 5 |
20 | simprr 484 | . . . . 5 | |
21 | 19, 20 | eqtr3d 2074 | . . . 4 |
22 | 21 | ex 108 | . . 3 |
23 | 6, 22 | mtoi 590 | . 2 |
24 | 23 | con2i 557 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wo 629 wceq 1243 wcel 1393 wrex 2307 crab 2310 c0 3224 csn 3375 cpr 3376 crio 5467 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-nul 3883 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-rab 2315 df-v 2559 df-dif 2920 df-nul 3225 df-sn 3381 df-uni 3581 df-iota 4867 df-riota 5468 |
This theorem is referenced by: acexmidlem1 5508 |
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