Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > caov12d | Unicode version |
Description: Rearrange arguments in a commutative, associative operation. (Contributed by NM, 26-Aug-1995.) (Revised by Mario Carneiro, 30-Dec-2014.) |
Ref | Expression |
---|---|
caovd.1 | |
caovd.2 | |
caovd.3 | |
caovd.com | |
caovd.ass |
Ref | Expression |
---|---|
caov12d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovd.com | . . . 4 | |
2 | caovd.1 | . . . 4 | |
3 | caovd.2 | . . . 4 | |
4 | 1, 2, 3 | caovcomd 5920 | . . 3 |
5 | 4 | oveq1d 5782 | . 2 |
6 | caovd.ass | . . 3 | |
7 | caovd.3 | . . 3 | |
8 | 6, 2, 3, 7 | caovassd 5923 | . 2 |
9 | 6, 3, 2, 7 | caovassd 5923 | . 2 |
10 | 5, 8, 9 | 3eqtr3d 2178 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 w3a 962 wceq 1331 wcel 1480 (class class class)co 5767 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-iota 5083 df-fv 5126 df-ov 5770 |
This theorem is referenced by: caov4d 5948 caovimo 5957 ltaddnq 7208 ltexnqq 7209 enq0tr 7235 mullocprlem 7371 1idprl 7391 1idpru 7392 cauappcvgprlemdisj 7452 mulcmpblnrlemg 7541 lttrsr 7563 ltsosr 7565 0idsr 7568 1idsr 7569 recexgt0sr 7574 mulgt0sr 7579 axmulass 7674 |
Copyright terms: Public domain | W3C validator |