Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 1288 | . . 3 | |
5 | caovass.4 | . . . . 5 | |
6 | 5 | a1i 9 | . . . 4 |
7 | 6 | caovassg 5679 | . . 3 |
8 | 4, 7 | mpan 414 | . 2 |
9 | 1, 2, 3, 8 | mp3an 1268 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 102 w3a 919 wceq 1284 wtru 1285 wcel 1433 cvv 2601 (class class class)co 5532 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-iota 4887 df-fv 4930 df-ov 5535 |
This theorem is referenced by: caov32 5708 caov12 5709 caov31 5710 caov13 5711 |
Copyright terms: Public domain | W3C validator |