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Theorem nfaov 41784
Description: Bound-variable hypothesis builder for operation value, analogous to nfov 6841. To prove a deduction version of this analogous to nfovd 6840 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 41741). (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 41723 . 2 ((𝐴𝐹𝐵)) = (𝐹'''⟨𝐴, 𝐵⟩)
2 nfaov.3 . . 3 𝑥𝐹
3 nfaov.2 . . . 4 𝑥𝐴
4 nfaov.4 . . . 4 𝑥𝐵
53, 4nfop 4570 . . 3 𝑥𝐴, 𝐵
62, 5nfafv 41741 . 2 𝑥(𝐹'''⟨𝐴, 𝐵⟩)
71, 6nfcxfr 2901 1 𝑥 ((𝐴𝐹𝐵))
Colors of variables: wff setvar class
Syntax hints:  wnfc 2890  cop 4328  '''cafv 41719   ((caov 41720
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1989  ax-6 2055  ax-7 2091  ax-9 2149  ax-10 2169  ax-11 2184  ax-12 2197  ax-13 2392  ax-ext 2741
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2048  df-clab 2748  df-cleq 2754  df-clel 2757  df-nfc 2892  df-ral 3056  df-rex 3057  df-rab 3060  df-v 3343  df-dif 3719  df-un 3721  df-in 3723  df-ss 3730  df-nul 4060  df-if 4232  df-sn 4323  df-pr 4325  df-op 4329  df-uni 4590  df-br 4806  df-opab 4866  df-xp 5273  df-rel 5274  df-cnv 5275  df-co 5276  df-dm 5277  df-res 5279  df-iota 6013  df-fun 6052  df-fv 6058  df-dfat 41721  df-afv 41722  df-aov 41723
This theorem is referenced by:  csbaovg  41785
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