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Theorem nfrexd 2666
 Description: Deduction version of nfrex 2669. (Contributed by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
nfrald.2 yφ
nfrald.3 (φxA)
nfrald.4 (φ → Ⅎxψ)
Assertion
Ref Expression
nfrexd (φ → Ⅎxy A ψ)

Proof of Theorem nfrexd
StepHypRef Expression
1 dfrex2 2627 . 2 (y A ψ ↔ ¬ y A ¬ ψ)
2 nfrald.2 . . . 4 yφ
3 nfrald.3 . . . 4 (φxA)
4 nfrald.4 . . . . 5 (φ → Ⅎxψ)
54nfnd 1791 . . . 4 (φ → Ⅎx ¬ ψ)
62, 3, 5nfrald 2665 . . 3 (φ → Ⅎxy A ¬ ψ)
76nfnd 1791 . 2 (φ → Ⅎx ¬ y A ¬ ψ)
81, 7nfxfrd 1571 1 (φ → Ⅎxy A ψ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  Ⅎwnf 1544  Ⅎwnfc 2476  ∀wral 2614  ∃wrex 2615 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620 This theorem is referenced by:  nfunid  3898
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