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Theorem hvmulcomi 22549
 Description: Scalar multiplication commutative law. (Contributed by NM, 3-Sep-1999.) (New usage is discouraged.)
Hypotheses
Ref Expression
hvmulcom.1
hvmulcom.2
hvmulcom.3
Assertion
Ref Expression
hvmulcomi

Proof of Theorem hvmulcomi
StepHypRef Expression
1 hvmulcom.1 . 2
2 hvmulcom.2 . 2
3 hvmulcom.3 . 2
4 hvmulcom 22545 . 2
51, 2, 3, 4mp3an 1279 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   wcel 1725  (class class class)co 6081  cc 8988  chil 22422   csm 22424 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-mulcom 9054  ax-hvmulass 22510 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-iota 5418  df-fv 5462  df-ov 6084
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