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Mirrors > Home > ILE Home > Th. List > mul32i | Unicode version |
Description: Commutative/associative law that swaps the last two factors in a triple product. (Contributed by NM, 11-May-1999.) |
Ref | Expression |
---|---|
mul.1 | |
mul.2 | |
mul.3 |
Ref | Expression |
---|---|
mul32i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mul.1 | . 2 | |
2 | mul.2 | . 2 | |
3 | mul.3 | . 2 | |
4 | mul32 8006 | . 2 | |
5 | 1, 2, 3, 4 | mp3an 1319 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1335 wcel 2128 (class class class)co 5825 cc 7731 cmul 7738 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 ax-mulcom 7834 ax-mulass 7836 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-v 2714 df-un 3106 df-sn 3566 df-pr 3567 df-op 3569 df-uni 3774 df-br 3967 df-iota 5136 df-fv 5179 df-ov 5828 |
This theorem is referenced by: 8th4div3 9053 |
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