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Theorem nf3and 1823
 Description: Deduction form of bound-variable hypothesis builder nf3an 1827. (Contributed by NM, 17-Feb-2013.) (Revised by Mario Carneiro, 16-Oct-2016.)
Hypotheses
Ref Expression
nfand.1 (φ → Ⅎxψ)
nfand.2 (φ → Ⅎxχ)
nfand.3 (φ → Ⅎxθ)
Assertion
Ref Expression
nf3and (φ → Ⅎx(ψ χ θ))

Proof of Theorem nf3and
StepHypRef Expression
1 df-3an 936 . 2 ((ψ χ θ) ↔ ((ψ χ) θ))
2 nfand.1 . . . 4 (φ → Ⅎxψ)
3 nfand.2 . . . 4 (φ → Ⅎxχ)
42, 3nfand 1822 . . 3 (φ → Ⅎx(ψ χ))
5 nfand.3 . . 3 (φ → Ⅎxθ)
64, 5nfand 1822 . 2 (φ → Ⅎx((ψ χ) θ))
71, 6nfxfrd 1571 1 (φ → Ⅎx(ψ χ θ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934  Ⅎwnf 1544 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-11 1746 This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936  df-ex 1542  df-nf 1545 This theorem is referenced by: (None)
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