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Mirrors > Home > ILE Home > Th. List > acexmidlemab | Unicode version |
Description: Lemma for acexmid 5850. (Contributed by Jim Kingdon, 6-Aug-2019.) |
Ref | Expression |
---|---|
acexmidlem.a | |
acexmidlem.b | |
acexmidlem.c |
Ref | Expression |
---|---|
acexmidlemab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3418 | . . . 4 | |
2 | 0ex 4114 | . . . . . 6 | |
3 | 2 | snid 3612 | . . . . 5 |
4 | eleq2 2234 | . . . . 5 | |
5 | 3, 4 | mpbiri 167 | . . . 4 |
6 | 1, 5 | mto 657 | . . 3 |
7 | acexmidlem.a | . . . . . . . . . 10 | |
8 | acexmidlem.b | . . . . . . . . . 10 | |
9 | acexmidlem.c | . . . . . . . . . 10 | |
10 | 7, 8, 9 | acexmidlemph 5844 | . . . . . . . . 9 |
11 | id 19 | . . . . . . . . . 10 | |
12 | eleq1 2233 | . . . . . . . . . . . 12 | |
13 | 12 | anbi1d 462 | . . . . . . . . . . 11 |
14 | 13 | rexbidv 2471 | . . . . . . . . . 10 |
15 | 11, 14 | riotaeqbidv 5810 | . . . . . . . . 9 |
16 | 10, 15 | syl 14 | . . . . . . . 8 |
17 | 16 | eqeq1d 2179 | . . . . . . 7 |
18 | 17 | biimpa 294 | . . . . . 6 |
19 | 18 | adantrr 476 | . . . . 5 |
20 | simprr 527 | . . . . 5 | |
21 | 19, 20 | eqtr3d 2205 | . . . 4 |
22 | 21 | ex 114 | . . 3 |
23 | 6, 22 | mtoi 659 | . 2 |
24 | 23 | con2i 622 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wo 703 wceq 1348 wcel 2141 wrex 2449 crab 2452 c0 3414 csn 3581 cpr 3582 crio 5806 |
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 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 ax-nul 4113 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-rab 2457 df-v 2732 df-dif 3123 df-nul 3415 df-sn 3587 df-uni 3795 df-iota 5158 df-riota 5807 |
This theorem is referenced by: acexmidlem1 5847 |
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