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Theorem nf3an 1827
 Description: If x is not free in φ, ψ, and χ, it is not free in (φ ∧ ψ ∧ χ). (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypotheses
Ref Expression
nfan.1 xφ
nfan.2 xψ
nfan.3 xχ
Assertion
Ref Expression
nf3an x(φ ψ χ)

Proof of Theorem nf3an
StepHypRef Expression
1 df-3an 936 . 2 ((φ ψ χ) ↔ ((φ ψ) χ))
2 nfan.1 . . . 4 xφ
3 nfan.2 . . . 4 xψ
42, 3nfan 1824 . . 3 x(φ ψ)
5 nfan.3 . . 3 xχ
64, 5nfan 1824 . 2 x((φ ψ) χ)
71, 6nfxfr 1570 1 x(φ ψ χ)
 Colors of variables: wff setvar class Syntax hints:   ∧ 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-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  hb3an  1830  vtocl3gaf  2923  mob  3018
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