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Theorem nfaov 39908
 Description: Bound-variable hypothesis builder for operation value, analogous to nfov 6575. To prove a deduction version of this analogous to nfovd 6574 is not quickly possible because many deduction versions for bound-variable hypothesis builder for constructs the definition of alternative operation values is based on are not available (see nfafv 39865). (Contributed by Alexander van der Vekens, 26-May-2017.)
Hypotheses
Ref Expression
nfaov.2 𝑥𝐴
nfaov.3 𝑥𝐹
nfaov.4 𝑥𝐵
Assertion
Ref Expression
nfaov 𝑥 ((𝐴𝐹𝐵))

Proof of Theorem nfaov
StepHypRef Expression
1 df-aov 39847 . 2 ((𝐴𝐹𝐵)) = (𝐹'''⟨𝐴, 𝐵⟩)
2 nfaov.3 . . 3 𝑥𝐹
3 nfaov.2 . . . 4 𝑥𝐴
4 nfaov.4 . . . 4 𝑥𝐵
53, 4nfop 4356 . . 3 𝑥𝐴, 𝐵
62, 5nfafv 39865 . 2 𝑥(𝐹'''⟨𝐴, 𝐵⟩)
71, 6nfcxfr 2749 1 𝑥 ((𝐴𝐹𝐵))
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnfc 2738  ⟨cop 4131  '''cafv 39843   ((caov 39844 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rex 2902  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-uni 4373  df-br 4584  df-opab 4644  df-xp 5044  df-rel 5045  df-cnv 5046  df-co 5047  df-dm 5048  df-res 5050  df-iota 5768  df-fun 5806  df-fv 5812  df-dfat 39845  df-afv 39846  df-aov 39847 This theorem is referenced by:  csbaovg  39909
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