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Mirrors > Home > HSE Home > Th. List > ax-hvmul0 | Structured version Visualization version Unicode version |
Description: Scalar multiplication by zero. We can derive the existence of the negative of a vector from this axiom (see hvsubid 27883 and hvsubval 27873). (Contributed by NM, 29-May-1999.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ax-hvmul0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 | |
2 | chil 27776 | . . 3 | |
3 | 1, 2 | wcel 1990 | . 2 |
4 | cc0 9936 | . . . 4 | |
5 | csm 27778 | . . . 4 | |
6 | 4, 1, 5 | co 6650 | . . 3 |
7 | c0v 27781 | . . 3 | |
8 | 6, 7 | wceq 1483 | . 2 |
9 | 3, 8 | wi 4 | 1 |
Colors of variables: wff setvar class |
This axiom is referenced by: hvmul0 27881 hvmul0or 27882 hvsubid 27883 hi01 27953 h1de2ctlem 28414 spansneleq 28429 h1datomi 28440 |
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