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Theorem cscval 28553
 Description: Value of the cosecant function. (Contributed by David A. Wheeler, 14-Mar-2014.)
Assertion
Ref Expression
cscval

Proof of Theorem cscval
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 fveq2 5730 . . . 4
21neeq1d 2616 . . 3
32elrab 3094 . 2
4 fveq2 5730 . . . 4
54oveq2d 6099 . . 3
6 df-csc 28550 . . 3
7 ovex 6108 . . 3
85, 6, 7fvmpt 5808 . 2
93, 8sylbir 206 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726   wne 2601  crab 2711  cfv 5456  (class class class)co 6083  cc 8990  cc0 8992  c1 8993   cdiv 9679  csin 12668  ccsc 28547 This theorem is referenced by:  csccl  28556  recsccl  28559  reccsc  28562  cotsqcscsq  28567 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-opab 4269  df-mpt 4270  df-id 4500  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-iota 5420  df-fun 5458  df-fv 5464  df-ov 6086  df-csc 28550
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