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Mirrors > Home > ILE Home > Th. List > ltordlem | Unicode version |
Description: Lemma for eqord1 8402. (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 2552 | . 2 |
3 | breq1 3992 | . . . 4 | |
4 | ltord.2 | . . . . 5 | |
5 | 4 | breq1d 3999 | . . . 4 |
6 | 3, 5 | imbi12d 233 | . . 3 |
7 | breq2 3993 | . . . 4 | |
8 | eqeq1 2177 | . . . . . . 7 | |
9 | ltord.1 | . . . . . . . 8 | |
10 | 9 | eqeq1d 2179 | . . . . . . 7 |
11 | 8, 10 | imbi12d 233 | . . . . . 6 |
12 | ltord.3 | . . . . . 6 | |
13 | 11, 12 | chvarv 1930 | . . . . 5 |
14 | 13 | breq2d 4001 | . . . 4 |
15 | 7, 14 | imbi12d 233 | . . 3 |
16 | 6, 15 | rspc2v 2847 | . 2 |
17 | 2, 16 | mpan9 279 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1348 wcel 2141 wral 2448 wss 3121 class class class wbr 3989 cr 7773 clt 7954 |
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 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 |
This theorem depends on definitions: df-bi 116 df-3an 975 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-v 2732 df-un 3125 df-sn 3589 df-pr 3590 df-op 3592 df-br 3990 |
This theorem is referenced by: eqord1 8402 |
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