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

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
nfaov.3
nfaov.4
Assertion
Ref Expression
nfaov (())

Proof of Theorem nfaov
StepHypRef Expression
1 df-aov 27952 . 2 (()) '''
2 nfaov.3 . . 3
3 nfaov.2 . . . 4
4 nfaov.4 . . . 4
53, 4nfop 4000 . . 3
62, 5nfafv 27976 . 2 '''
71, 6nfcxfr 2569 1 (())
 Colors of variables: wff set class Syntax hints:  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
 Copyright terms: Public domain W3C validator