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Theorem nfaov 28019
Description: Bound-variable hypothesis builder for operation value, analogous to nfov 6104. To prove a deduction version of this analogous to nfovd 6103 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 27976). (Contributed by Alexander van der Vekens, 26-May-2017.)
Hypotheses
Ref Expression
nfaov.2  |-  F/_ x A
nfaov.3  |-  F/_ x F
nfaov.4  |-  F/_ x B
Assertion
Ref Expression
nfaov  |-  F/_ x (( A F B))

Proof of Theorem nfaov
StepHypRef Expression
1 df-aov 27952 . 2  |- (( A F B))  =  ( F''' <. A ,  B >. )
2 nfaov.3 . . 3  |-  F/_ x F
3 nfaov.2 . . . 4  |-  F/_ x A
4 nfaov.4 . . . 4  |-  F/_ x B
53, 4nfop 4000 . . 3  |-  F/_ x <. A ,  B >.
62, 5nfafv 27976 . 2  |-  F/_ x
( F''' <. A ,  B >. )
71, 6nfcxfr 2569 1  |-  F/_ x (( A F B))
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2559   <.cop 3817  '''cafv 27948   ((caov 27949
This theorem is referenced by:  csbaovg  28020
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-res 4890  df-iota 5418  df-fun 5456  df-fv 5462  df-dfat 27950  df-afv 27951  df-aov 27952
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