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Axiom ax-hvmul0 27033
Description: Scalar multiplication by zero. We can derive the existence of the negative of a vector from this axiom (see hvsubid 27049 and hvsubval 27039). (Contributed by NM, 29-May-1999.) (New usage is discouraged.)
Assertion
Ref Expression
ax-hvmul0 (𝐴 ∈ ℋ → (0 · 𝐴) = 0)

Detailed syntax breakdown of Axiom ax-hvmul0
StepHypRef Expression
1 cA . . 3 class 𝐴
2 chil 26942 . . 3 class
31, 2wcel 1938 . 2 wff 𝐴 ∈ ℋ
4 cc0 9695 . . . 4 class 0
5 csm 26944 . . . 4 class ·
64, 1, 5co 6431 . . 3 class (0 · 𝐴)
7 c0v 26947 . . 3 class 0
86, 7wceq 1474 . 2 wff (0 · 𝐴) = 0
93, 8wi 4 1 wff (𝐴 ∈ ℋ → (0 · 𝐴) = 0)
Colors of variables: wff setvar class
This axiom is referenced by:  hvmul0  27047  hvmul0or  27048  hvsubid  27049  hi01  27119  h1de2ctlem  27580  spansneleq  27595  h1datomi  27606
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