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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 2492 | . 2 |
3 | breq1 3902 | . . . 4 | |
4 | breq1 3902 | . . . . 5 | |
5 | 4 | orbi1d 765 | . . . 4 |
6 | 3, 5 | imbi12d 233 | . . 3 |
7 | breq2 3903 | . . . 4 | |
8 | breq2 3903 | . . . . 5 | |
9 | 8 | orbi2d 764 | . . . 4 |
10 | 7, 9 | imbi12d 233 | . . 3 |
11 | breq2 3903 | . . . . 5 | |
12 | breq1 3902 | . . . . 5 | |
13 | 11, 12 | orbi12d 767 | . . . 4 |
14 | 13 | imbi2d 229 | . . 3 |
15 | 6, 10, 14 | rspc3v 2779 | . 2 |
16 | 2, 15 | mpan9 279 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wo 682 w3a 947 wceq 1316 wcel 1465 wral 2393 class class class wbr 3899 |
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-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 |
This theorem is referenced by: swoer 6425 swoord1 6426 swoord2 6427 |
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