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Theorem tanhval-named 28482
 Description: Value of the named tanh function. Here we show the simple conversion to the conventional form used in set.mm, using the definition given by df-tanh 28479. (Contributed by David A. Wheeler, 10-May-2015.)
Assertion
Ref Expression
tanhval-named cosh tanh

Proof of Theorem tanhval-named
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 oveq2 6090 . . . 4
21fveq2d 5733 . . 3
32oveq1d 6097 . 2
4 df-tanh 28479 . 2 tanh cosh
5 ovex 6107 . 2
63, 4, 5fvmpt 5807 1 cosh tanh
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653   wcel 1726   cdif 3318  csn 3815  ccnv 4878  cima 4882  cfv 5455  (class class class)co 6082  cc 8989  cc0 8991  ci 8993   cmul 8996   cdiv 9678  ctan 12669  coshccosh 28475  tanhctanh 28476 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 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404 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 2286  df-mo 2287  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-sbc 3163  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-uni 4017  df-br 4214  df-opab 4268  df-mpt 4269  df-id 4499  df-xp 4885  df-rel 4886  df-cnv 4887  df-co 4888  df-dm 4889  df-iota 5419  df-fun 5457  df-fv 5463  df-ov 6085  df-tanh 28479
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