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Axiom ax-his1 23606
Description: Conjugate law for inner product. Postulate (S1) of [Beran] p. 95. Note that ` is the complex conjugate cjval 12438 of . In the literature, the inner product of and is usually written , but our operation notation co 6103 allows us to use existing theorems about operations and also avoids a clash with the definition of an ordered pair df-op 3918. Physicists use <.B|A>., called Dirac bra-ket notation, to represent this operation; see comments in df-bra 24376. (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 23443 . . . 4
31, 2wcel 1732 . . 3
4 cB . . . 4
54, 2wcel 1732 . . 3
63, 5wa 360 . 2
7 csp 23446 . . . 4
81, 4, 7co 6103 . . 3
94, 1, 7co 6103 . . . 4
10 ccj 12432 . . . 4
119, 10cfv 5438 . . 3
128, 11wceq 1670 . 2
136, 12wi 4 1
Colors of variables: wff set class
This axiom is referenced by:  his5  23610  his7  23614  his2sub2  23617  hire  23618  hi02  23621  his1i  23624  abshicom  23625  hial2eq2  23631  orthcom  23632  adjsym  24359  cnvadj  24418  adj2  24460
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