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Mirrors > Home > ILE Home > Th. List > ltordlem | Unicode version |
Description: Lemma for eqord1 8353. (Contributed by Mario Carneiro, 14-Jun-2014.) |
Ref | Expression |
---|---|
ltord.1 | |
ltord.2 | |
ltord.3 | |
ltord.4 | |
ltord.5 | |
ltord.6 |
Ref | Expression |
---|---|
ltordlem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltord.6 | . . 3 | |
2 | 1 | ralrimivva 2539 | . 2 |
3 | breq1 3968 | . . . 4 | |
4 | ltord.2 | . . . . 5 | |
5 | 4 | breq1d 3975 | . . . 4 |
6 | 3, 5 | imbi12d 233 | . . 3 |
7 | breq2 3969 | . . . 4 | |
8 | eqeq1 2164 | . . . . . . 7 | |
9 | ltord.1 | . . . . . . . 8 | |
10 | 9 | eqeq1d 2166 | . . . . . . 7 |
11 | 8, 10 | imbi12d 233 | . . . . . 6 |
12 | ltord.3 | . . . . . 6 | |
13 | 11, 12 | chvarv 1917 | . . . . 5 |
14 | 13 | breq2d 3977 | . . . 4 |
15 | 7, 14 | imbi12d 233 | . . 3 |
16 | 6, 15 | rspc2v 2829 | . 2 |
17 | 2, 16 | mpan9 279 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wcel 2128 wral 2435 wss 3102 class class class wbr 3965 cr 7726 clt 7907 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-v 2714 df-un 3106 df-sn 3566 df-pr 3567 df-op 3569 df-br 3966 |
This theorem is referenced by: eqord1 8353 |
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