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Theorem nfaov 47129
Description: Bound-variable hypothesis builder for operation value, analogous to nfov 7461. To prove a deduction version of this analogous to nfovd 7460 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 47086). (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 47071 . 2 ((𝐴𝐹𝐵)) = (𝐹'''⟨𝐴, 𝐵⟩)
2 nfaov.3 . . 3 𝑥𝐹
3 nfaov.2 . . . 4 𝑥𝐴
4 nfaov.4 . . . 4 𝑥𝐵
53, 4nfop 4894 . . 3 𝑥𝐴, 𝐵
62, 5nfafv 47086 . 2 𝑥(𝐹'''⟨𝐴, 𝐵⟩)
71, 6nfcxfr 2901 1 𝑥 ((𝐴𝐹𝐵))
Colors of variables: wff setvar class
Syntax hints:  wnfc 2888  cop 4637  '''cafv 47067   ((caov 47068
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706  ax-sep 5302  ax-nul 5312  ax-pr 5438
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-nf 1781  df-sb 2063  df-mo 2538  df-eu 2567  df-clab 2713  df-cleq 2727  df-clel 2814  df-nfc 2890  df-ne 2939  df-ral 3060  df-rex 3069  df-rab 3434  df-v 3480  df-sbc 3792  df-csb 3909  df-dif 3966  df-un 3968  df-in 3970  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-int 4952  df-br 5149  df-opab 5211  df-id 5583  df-xp 5695  df-rel 5696  df-cnv 5697  df-co 5698  df-dm 5699  df-res 5701  df-iota 6516  df-fun 6565  df-fv 6571  df-aiota 47035  df-dfat 47069  df-afv 47070  df-aov 47071
This theorem is referenced by:  csbaovg  47130
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