Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > mul4d | Unicode version |
Description: Rearrangement of 4 factors. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
muld.1 | |
addcomd.2 | |
mul12d.3 | |
mul4d.4 |
Ref | Expression |
---|---|
mul4d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | muld.1 | . 2 | |
2 | addcomd.2 | . 2 | |
3 | mul12d.3 | . 2 | |
4 | mul4d.4 | . 2 | |
5 | mul4 7145 | . 2 | |
6 | 1, 2, 3, 4, 5 | syl22anc 1136 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1243 wcel 1393 (class class class)co 5512 cc 6887 cmul 6894 |
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 ax-mulcl 6982 ax-mulcom 6985 ax-mulass 6987 |
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-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: mulreim 7595 remullem 9471 absmul 9667 |
Copyright terms: Public domain | W3C validator |