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Mirrors > Home > ILE Home > Th. List > caovord3 | Unicode version |
Description: Ordering law. (Contributed by NM, 29-Feb-1996.) |
Ref | Expression |
---|---|
caovord.1 | |
caovord.2 | |
caovord.3 | |
caovord2.3 | |
caovord2.com | |
caovord3.4 |
Ref | Expression |
---|---|
caovord3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovord.1 | . . . . 5 | |
2 | caovord2.3 | . . . . 5 | |
3 | caovord.3 | . . . . 5 | |
4 | caovord.2 | . . . . 5 | |
5 | caovord2.com | . . . . 5 | |
6 | 1, 2, 3, 4, 5 | caovord2 5993 | . . . 4 |
7 | 6 | adantr 274 | . . 3 |
8 | breq1 3968 | . . 3 | |
9 | 7, 8 | sylan9bb 458 | . 2 |
10 | caovord3.4 | . . . 4 | |
11 | 10, 4, 3 | caovord 5992 | . . 3 |
12 | 11 | ad2antlr 481 | . 2 |
13 | 9, 12 | bitr4d 190 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wcel 2128 cvv 2712 class class class wbr 3965 (class class class)co 5824 |
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-rex 2441 df-v 2714 df-un 3106 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3773 df-br 3966 df-iota 5135 df-fv 5178 df-ov 5827 |
This theorem is referenced by: (None) |
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