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Theorem nfovd 5477
Description: Deduction version of bound-variable hypothesis builder nfov 5478. (Contributed by NM, 13-Dec-2005.) (Proof shortened by Andrew Salmon, 22-Oct-2011.)
Hypotheses
Ref Expression
nfovd.2 (φxA)
nfovd.3 (φx𝐹)
nfovd.4 (φxB)
Assertion
Ref Expression
nfovd (φx(A𝐹B))

Proof of Theorem nfovd
StepHypRef Expression
1 df-ov 5458 . 2 (A𝐹B) = (𝐹‘⟨A, B⟩)
2 nfovd.3 . . 3 (φx𝐹)
3 nfovd.2 . . . 4 (φxA)
4 nfovd.4 . . . 4 (φxB)
53, 4nfopd 3557 . . 3 (φxA, B⟩)
62, 5nffvd 5130 . 2 (φx(𝐹‘⟨A, B⟩))
71, 6nfcxfrd 2173 1 (φx(A𝐹B))
Colors of variables: wff set class
Syntax hints:  wi 4  wnfc 2162  cop 3370  cfv 4845  (class class class)co 5455
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853  df-ov 5458
This theorem is referenced by:  nfov  5478  nfnegd  7004
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