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Theorem aoveq123d 28146
 Description: Equality deduction for operation value, analogous to oveq123d 5895. (Contributed by Alexander van der Vekens, 26-May-2017.)
Hypotheses
Ref Expression
aoveq123d.1
aoveq123d.2
aoveq123d.3
Assertion
Ref Expression
aoveq123d (()) (())

Proof of Theorem aoveq123d
StepHypRef Expression
1 aoveq123d.1 . . 3
2 aoveq123d.2 . . . 4
3 aoveq123d.3 . . . 4
42, 3opeq12d 3820 . . 3
51, 4afveq12d 28101 . 2 ''' '''
6 df-aov 28079 . 2 (()) '''
7 df-aov 28079 . 2 (()) '''
85, 6, 73eqtr4g 2353 1 (()) (())
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1632  cop 3656  '''cafv 28075   ((caov 28076 This theorem is referenced by:  csbaovg  28148  rspceaov  28165  faovcl  28168 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-opab 4094  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-res 4717  df-iota 5235  df-fun 5273  df-fv 5279  df-dfat 28077  df-afv 28078  df-aov 28079
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