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Definition df-h0v 28674
Description: Define the zero vector of Hilbert space. Note that 0vec is considered a primitive in the Hilbert space axioms below, and we don't use this definition outside of this section. It is proved from the axioms as theorem hh0v 28872. (Contributed by NM, 31-May-2008.) (New usage is discouraged.)
Assertion
Ref Expression
df-h0v 0 = (0vec‘⟨⟨ + , · ⟩, norm⟩)

Detailed syntax breakdown of Definition df-h0v
StepHypRef Expression
1 c0v 28628 . 2 class 0
2 cva 28624 . . . . 5 class +
3 csm 28625 . . . . 5 class ·
42, 3cop 4563 . . . 4 class ⟨ + , ·
5 cno 28627 . . . 4 class norm
64, 5cop 4563 . . 3 class ⟨⟨ + , · ⟩, norm
7 cn0v 28292 . . 3 class 0vec
86, 7cfv 6348 . 2 class (0vec‘⟨⟨ + , · ⟩, norm⟩)
91, 8wceq 1528 1 wff 0 = (0vec‘⟨⟨ + , · ⟩, norm⟩)
Colors of variables: wff setvar class
This definition is referenced by:  axhv0cl-zf  28689  axhvaddid-zf  28690  axhvmul0-zf  28696  axhis4-zf  28701
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