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Theorem nfrexg 3269
 Description: Bound-variable hypothesis builder for restricted quantification. Usage of this theorem is discouraged because it depends on ax-13 2379. See nfrex 3268 for a version with a disjoint variable condition, but not requiring ax-13 2379. (Contributed by NM, 1-Sep-1999.) (Revised by Mario Carneiro, 7-Oct-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2019.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfrexg.1 𝑥𝐴
nfrexg.2 𝑥𝜑
Assertion
Ref Expression
nfrexg 𝑥𝑦𝐴 𝜑

Proof of Theorem nfrexg
StepHypRef Expression
1 nftru 1806 . . 3 𝑦
2 nfrexg.1 . . . 4 𝑥𝐴
32a1i 11 . . 3 (⊤ → 𝑥𝐴)
4 nfrexg.2 . . . 4 𝑥𝜑
54a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
61, 3, 5nfrexdg 3267 . 2 (⊤ → Ⅎ𝑥𝑦𝐴 𝜑)
76mptru 1545 1 𝑥𝑦𝐴 𝜑
 Colors of variables: wff setvar class Syntax hints:  ⊤wtru 1539  Ⅎwnf 1785  Ⅎwnfc 2936  ∃wrex 3107 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-13 2379  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-cleq 2791  df-clel 2870  df-nfc 2938  df-ral 3111  df-rex 3112 This theorem is referenced by:  nfiung  4914
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