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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 1247 | . . 3 | |
5 | caovass.4 | . . . . 5 | |
6 | 5 | a1i 9 | . . . 4 |
7 | 6 | caovassg 5659 | . . 3 |
8 | 4, 7 | mpan 400 | . 2 |
9 | 1, 2, 3, 8 | mp3an 1232 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 w3a 885 wceq 1243 wtru 1244 wcel 1393 cvv 2557 (class class class)co 5512 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-rex 2312 df-v 2559 df-un 2922 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-iota 4867 df-fv 4910 df-ov 5515 |
This theorem is referenced by: caov32 5688 caov12 5689 caov31 5690 caov13 5691 |
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