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Theorem mul32i 7629
 Description: Commutative/associative law that swaps the last two factors in a triple product. (Contributed by NM, 11-May-1999.)
Hypotheses
Ref Expression
mul.1
mul.2
mul.3
Assertion
Ref Expression
mul32i

Proof of Theorem mul32i
StepHypRef Expression
1 mul.1 . 2
2 mul.2 . 2
3 mul.3 . 2
4 mul32 7612 . 2
51, 2, 3, 4mp3an 1273 1
 Colors of variables: wff set class Syntax hints:   wceq 1289   wcel 1438  (class class class)co 5652  cc 7348   cmul 7355 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-mulcom 7446  ax-mulass 7448 This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365  df-v 2621  df-un 3003  df-sn 3452  df-pr 3453  df-op 3455  df-uni 3654  df-br 3846  df-iota 4980  df-fv 5023  df-ov 5655 This theorem is referenced by:  8th4div3  8635
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