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Theorem nfbrd 3798
Description: Deduction version of bound-variable hypothesis builder nfbr 3799. (Contributed by NM, 13-Dec-2005.) (Revised by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
nfbrd.2 (φxA)
nfbrd.3 (φx𝑅)
nfbrd.4 (φxB)
Assertion
Ref Expression
nfbrd (φ → Ⅎx A𝑅B)

Proof of Theorem nfbrd
StepHypRef Expression
1 df-br 3756 . 2 (A𝑅B ↔ ⟨A, B 𝑅)
2 nfbrd.2 . . . 4 (φxA)
3 nfbrd.4 . . . 4 (φxB)
42, 3nfopd 3557 . . 3 (φxA, B⟩)
5 nfbrd.3 . . 3 (φx𝑅)
64, 5nfeld 2190 . 2 (φ → ℲxA, B 𝑅)
71, 6nfxfrd 1361 1 (φ → Ⅎx A𝑅B)
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1346   wcel 1390  wnfc 2162  cop 3370   class class class wbr 3755
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-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756
This theorem is referenced by:  nfbr  3799
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