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Mirrors > Home > ILE Home > Th. List > swopolem | Unicode version |
Description: Perform the substitutions into the strict weak ordering law. (Contributed by Mario Carneiro, 31-Dec-2014.) |
Ref | Expression |
---|---|
swopolem.1 |
Ref | Expression |
---|---|
swopolem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | swopolem.1 | . . 3 | |
2 | 1 | ralrimivvva 2402 | . 2 |
3 | breq1 3767 | . . . 4 | |
4 | breq1 3767 | . . . . 5 | |
5 | 4 | orbi1d 705 | . . . 4 |
6 | 3, 5 | imbi12d 223 | . . 3 |
7 | breq2 3768 | . . . 4 | |
8 | breq2 3768 | . . . . 5 | |
9 | 8 | orbi2d 704 | . . . 4 |
10 | 7, 9 | imbi12d 223 | . . 3 |
11 | breq2 3768 | . . . . 5 | |
12 | breq1 3767 | . . . . 5 | |
13 | 11, 12 | orbi12d 707 | . . . 4 |
14 | 13 | imbi2d 219 | . . 3 |
15 | 6, 10, 14 | rspc3v 2665 | . 2 |
16 | 2, 15 | mpan9 265 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wo 629 w3a 885 wceq 1243 wcel 1393 wral 2306 class class class wbr 3764 |
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-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 |
This theorem depends on definitions: df-bi 110 df-3an 887 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-v 2559 df-un 2922 df-sn 3381 df-pr 3382 df-op 3384 df-br 3765 |
This theorem is referenced by: swoer 6134 swoord1 6135 swoord2 6136 |
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