![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > caovcomd | Unicode version |
Description: Convert an operation commutative law to class notation. (Contributed by Mario Carneiro, 30-Dec-2014.) |
Ref | Expression |
---|---|
caovcomg.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
caovcomd.2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
caovcomd.3 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
caovcomd |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() | |
2 | caovcomd.2 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | caovcomd.3 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | caovcomg.1 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 4 | caovcomg 6074 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | 1, 2, 3, 5 | syl12anc 1247 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2175 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-ral 2477 df-rex 2478 df-v 2762 df-un 3157 df-sn 3624 df-pr 3625 df-op 3627 df-uni 3836 df-br 4030 df-iota 5215 df-fv 5262 df-ov 5921 |
This theorem is referenced by: caovcanrd 6082 caovord2d 6088 caovdir2d 6095 caov32d 6099 caov12d 6100 caov31d 6101 caov411d 6104 caov42d 6105 caovimo 6112 ecopovsymg 6688 ecopoverg 6690 ltsonq 7458 prarloclemlo 7554 addextpr 7681 ltsosr 7824 ltasrg 7830 mulextsr1lem 7840 seq3f1olemqsumkj 10582 seqf1oglem2a 10589 |
Copyright terms: Public domain | W3C validator |