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Theorem aovnuoveq 28022
 Description: The alternative value of the operation on an ordered pair equals the operation's value at this ordered pair. (Contributed by Alexander van der Vekens, 26-May-2017.)
Assertion
Ref Expression
aovnuoveq (()) (())

Proof of Theorem aovnuoveq
StepHypRef Expression
1 df-aov 27943 . . 3 (()) '''
21neeq1i 2608 . 2 (()) '''
3 afvnufveq 27978 . . 3 ''' '''
4 df-ov 6076 . . 3
53, 1, 43eqtr4g 2492 . 2 ''' (())
62, 5sylbi 188 1 (()) (())
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wne 2598  cvv 2948  cop 3809  cfv 5446  (class class class)co 6073  '''cafv 27939   ((caov 27940 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-rab 2706  df-v 2950  df-un 3317  df-if 3732  df-fv 5454  df-ov 6076  df-afv 27942  df-aov 27943
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