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Mirrors > Home > ILE Home > Th. List > caovass | Unicode version |
Description: Convert an operation associative law to class notation. (Contributed by NM, 26-Aug-1995.) (Revised by Mario Carneiro, 26-May-2014.) |
Ref | Expression |
---|---|
caovass.1 | |
caovass.2 | |
caovass.3 | |
caovass.4 |
Ref | Expression |
---|---|
caovass |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovass.1 | . 2 | |
2 | caovass.2 | . 2 | |
3 | caovass.3 | . 2 | |
4 | tru 1320 | . . 3 | |
5 | caovass.4 | . . . . 5 | |
6 | 5 | a1i 9 | . . . 4 |
7 | 6 | caovassg 5897 | . . 3 |
8 | 4, 7 | mpan 420 | . 2 |
9 | 1, 2, 3, 8 | mp3an 1300 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 w3a 947 wceq 1316 wtru 1317 wcel 1465 cvv 2660 (class class class)co 5742 |
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-rex 2399 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-iota 5058 df-fv 5101 df-ov 5745 |
This theorem is referenced by: caov32 5926 caov12 5927 caov31 5928 caov13 5929 |
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