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Theorem mul32i 9810
 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 9781 . 2
51, 2, 3, 4mp3an 1326 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1405   wcel 1842  (class class class)co 6278  cc 9520   cmul 9527 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-mulcom 9586  ax-mulass 9588 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-rex 2760  df-rab 2763  df-v 3061  df-dif 3417  df-un 3419  df-in 3421  df-ss 3428  df-nul 3739  df-if 3886  df-sn 3973  df-pr 3975  df-op 3979  df-uni 4192  df-br 4396  df-iota 5533  df-fv 5577  df-ov 6281 This theorem is referenced by:  8th4div3  10800  faclbnd4lem1  12415  bpoly4  14004  dec5nprm  14761  dec2nprm  14762  karatsuba  14779  quart1lem  23511  log2ublem2  23603  log2ub  23605  normlem3  26443  bcseqi  26451
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