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Theorem atans 20772
 Description: The "domain of continuity" of the arctangent. (Contributed by Mario Carneiro, 7-Apr-2015.)
Hypotheses
Ref Expression
atansopn.d
atansopn.s
Assertion
Ref Expression
atans
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem atans
StepHypRef Expression
1 oveq1 6090 . . . 4
21oveq2d 6099 . . 3
32eleq1d 2504 . 2
4 atansopn.s . 2
53, 4elrab2 3096 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   wceq 1653   wcel 1726  crab 2711   cdif 3319  (class class class)co 6083  cc 8990  cc0 8992  c1 8993   caddc 8995   cmnf 9120  c2 10051  cioc 10919  cexp 11384 This theorem is referenced by:  atans2  20773 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-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 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-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-rab 2716  df-v 2960  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-iota 5420  df-fv 5464  df-ov 6086
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