Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > caovcanrd | Unicode version |
Description: Commute the arguments of an operation cancellation law. (Contributed by Mario Carneiro, 30-Dec-2014.) |
Ref | Expression |
---|---|
caovcang.1 | |
caovcand.2 | |
caovcand.3 | |
caovcand.4 | |
caovcanrd.5 | |
caovcanrd.6 |
Ref | Expression |
---|---|
caovcanrd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovcanrd.6 | . . . 4 | |
2 | caovcanrd.5 | . . . 4 | |
3 | caovcand.3 | . . . 4 | |
4 | 1, 2, 3 | caovcomd 5998 | . . 3 |
5 | caovcand.4 | . . . 4 | |
6 | 1, 2, 5 | caovcomd 5998 | . . 3 |
7 | 4, 6 | eqeq12d 2180 | . 2 |
8 | caovcang.1 | . . 3 | |
9 | caovcand.2 | . . 3 | |
10 | 8, 9, 3, 5 | caovcand 6004 | . 2 |
11 | 7, 10 | bitr3d 189 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 968 wceq 1343 wcel 2136 (class class class)co 5842 |
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 1435 ax-7 1436 ax-gen 1437 ax-ie1 1481 ax-ie2 1482 ax-8 1492 ax-10 1493 ax-11 1494 ax-i12 1495 ax-bndl 1497 ax-4 1498 ax-17 1514 ax-i9 1518 ax-ial 1522 ax-i5r 1523 ax-ext 2147 |
This theorem depends on definitions: df-bi 116 df-3an 970 df-tru 1346 df-nf 1449 df-sb 1751 df-clab 2152 df-cleq 2158 df-clel 2161 df-nfc 2297 df-ral 2449 df-rex 2450 df-v 2728 df-un 3120 df-sn 3582 df-pr 3583 df-op 3585 df-uni 3790 df-br 3983 df-iota 5153 df-fv 5196 df-ov 5845 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |