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Mirrors > Home > ILE Home > Th. List > acexmidlema | Unicode version |
Description: Lemma for acexmid 5773. (Contributed by Jim Kingdon, 6-Aug-2019.) |
Ref | Expression |
---|---|
acexmidlem.a | |
acexmidlem.b | |
acexmidlem.c |
Ref | Expression |
---|---|
acexmidlema |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | acexmidlem.a | . . . 4 | |
2 | 1 | eleq2i 2206 | . . 3 |
3 | p0ex 4112 | . . . . 5 | |
4 | 3 | prid2 3630 | . . . 4 |
5 | eqeq1 2146 | . . . . . 6 | |
6 | 5 | orbi1d 780 | . . . . 5 |
7 | 6 | elrab3 2841 | . . . 4 |
8 | 4, 7 | ax-mp 5 | . . 3 |
9 | 2, 8 | bitri 183 | . 2 |
10 | noel 3367 | . . . 4 | |
11 | 0ex 4055 | . . . . . 6 | |
12 | 11 | snid 3556 | . . . . 5 |
13 | eleq2 2203 | . . . . 5 | |
14 | 12, 13 | mpbii 147 | . . . 4 |
15 | 10, 14 | mto 651 | . . 3 |
16 | orel1 714 | . . 3 | |
17 | 15, 16 | ax-mp 5 | . 2 |
18 | 9, 17 | sylbi 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wo 697 wceq 1331 wcel 1480 crab 2420 c0 3363 csn 3527 cpr 3528 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-nul 4054 ax-pow 4098 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rab 2425 df-v 2688 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-nul 3364 df-pw 3512 df-sn 3533 df-pr 3534 |
This theorem is referenced by: acexmidlem1 5770 |
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