Users' Mathboxes Mathbox for Alexander van der Vekens < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  nfaov Unicode version

Theorem nfaov 28039
Description: Bound-variable hypothesis builder for operation value, analogous to nfov 5881. To prove a deduction version of this analogous to nfovd 5880 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 27999). (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 27976 . 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 3812 . . 3  |-  F/_ x <. A ,  B >.
62, 5nfafv 27999 . 2  |-  F/_ x
( F''' <. A ,  B >. )
71, 6nfcxfr 2416 1  |-  F/_ x (( A F B))
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2406   <.cop 3643  '''cafv 27972   ((caov 27973
This theorem is referenced by:  csbaovg  28040
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pow 4188  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702  df-iota 5219  df-fun 5257  df-fv 5263  df-dfat 27974  df-afv 27975  df-aov 27976
  Copyright terms: Public domain W3C validator