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Axiom ax-his1 23094
Description: Conjugate law for inner product. Postulate (S1) of [Beran] p. 95. Note that ` is the complex conjugate cjval 12377 of . In the literature, the inner product of and is usually written , but our operation notation co 6067 allows us to use existing theorems about operations and also avoids a clash with the definition of an ordered pair df-op 3903. Physicists use <.B|A>., called Dirac bra-ket notation, to represent this operation; see comments in df-bra 23864. (Contributed by NM, 29-Jul-1999.) (New usage is discouraged.)
Assertion
Ref Expression
ax-his1

Detailed syntax breakdown of Axiom ax-his1
StepHypRef Expression
1 cA . . . 4
2 chil 22931 . . . 4
31, 2wcel 1724 . . 3
4 cB . . . 4
54, 2wcel 1724 . . 3
63, 5wa 360 . 2
7 csp 22934 . . . 4
81, 4, 7co 6067 . . 3
94, 1, 7co 6067 . . . 4
10 ccj 12371 . . . 4
119, 10cfv 5417 . . 3
128, 11wceq 1662 . 2
136, 12wi 4 1
Colors of variables: wff set class
This axiom is referenced by:  his5  23098  his7  23102  his2sub2  23105  hire  23106  hi02  23109  his1i  23112  abshicom  23113  hial2eq2  23119  orthcom  23120  adjsym  23847  cnvadj  23906  adj2  23948
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