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Axiom ax-his1 22620
Description: Conjugate law for inner product. Postulate (S1) of [Beran] p. 95. Note that ` is the complex conjugate cjval 11962 of . In the literature, the inner product of and is usually written , but our operation notation co 6133 allows us to use existing theorems about operations and also avoids a clash with the definition of an ordered pair df-op 3854. Physicists use <. | >., called Dirac bra-ket notation, to represent this operation; see comments in df-bra 23389. (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 22458 . . . 4
31, 2wcel 1728 . . 3
4 cB . . . 4
54, 2wcel 1728 . . 3
63, 5wa 360 . 2
7 csp 22461 . . . 4
81, 4, 7co 6133 . . 3
94, 1, 7co 6133 . . . 4
10 ccj 11956 . . . 4
119, 10cfv 5505 . . 3
128, 11wceq 1654 . 2
136, 12wi 4 1
Colors of variables: wff set class
This axiom is referenced by:  his5  22624  his7  22628  his2sub2  22631  hire  22632  hi02  22635  his1i  22638  abshicom  22639  hial2eq2  22645  orthcom  22646  adjsym  23372  cnvadj  23431  adj2  23473
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