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Mirrors > Home > ILE Home > Th. List > acexmidlemab | Unicode version |
Description: Lemma for acexmid 5531. (Contributed by Jim Kingdon, 6-Aug-2019.) |
Ref | Expression |
---|---|
acexmidlem.a | |
acexmidlem.b | |
acexmidlem.c |
Ref | Expression |
---|---|
acexmidlemab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3255 | . . . 4 | |
2 | 0ex 3905 | . . . . . 6 | |
3 | 2 | snid 3425 | . . . . 5 |
4 | eleq2 2142 | . . . . 5 | |
5 | 3, 4 | mpbiri 166 | . . . 4 |
6 | 1, 5 | mto 620 | . . 3 |
7 | acexmidlem.a | . . . . . . . . . 10 | |
8 | acexmidlem.b | . . . . . . . . . 10 | |
9 | acexmidlem.c | . . . . . . . . . 10 | |
10 | 7, 8, 9 | acexmidlemph 5525 | . . . . . . . . 9 |
11 | id 19 | . . . . . . . . . 10 | |
12 | eleq1 2141 | . . . . . . . . . . . 12 | |
13 | 12 | anbi1d 452 | . . . . . . . . . . 11 |
14 | 13 | rexbidv 2369 | . . . . . . . . . 10 |
15 | 11, 14 | riotaeqbidv 5491 | . . . . . . . . 9 |
16 | 10, 15 | syl 14 | . . . . . . . 8 |
17 | 16 | eqeq1d 2089 | . . . . . . 7 |
18 | 17 | biimpa 290 | . . . . . 6 |
19 | 18 | adantrr 462 | . . . . 5 |
20 | simprr 498 | . . . . 5 | |
21 | 19, 20 | eqtr3d 2115 | . . . 4 |
22 | 21 | ex 113 | . . 3 |
23 | 6, 22 | mtoi 622 | . 2 |
24 | 23 | con2i 589 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 wo 661 wceq 1284 wcel 1433 wrex 2349 crab 2352 c0 3251 csn 3398 cpr 3399 crio 5487 |
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 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-nul 3904 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-rab 2357 df-v 2603 df-dif 2975 df-nul 3252 df-sn 3404 df-uni 3602 df-iota 4887 df-riota 5488 |
This theorem is referenced by: acexmidlem1 5528 |
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