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Theorem aoveq123d 38550
 Description: Equality deduction for operation value, analogous to oveq123d 6326. (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 4195 . . 3
51, 4afveq12d 38505 . 2 ''' '''
6 df-aov 38490 . 2 (()) '''
7 df-aov 38490 . 2 (()) '''
85, 6, 73eqtr4g 2488 1 (()) (())
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1437  cop 4004  '''cafv 38486   ((caov 38487 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-rex 2777  df-rab 2780  df-v 3082  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-if 3912  df-sn 3999  df-pr 4001  df-op 4005  df-uni 4220  df-br 4424  df-opab 4483  df-xp 4859  df-rel 4860  df-cnv 4861  df-co 4862  df-dm 4863  df-res 4865  df-iota 5565  df-fun 5603  df-fv 5609  df-dfat 38488  df-afv 38489  df-aov 38490 This theorem is referenced by:  csbaovg  38552  rspceaov  38569  faovcl  38572
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