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Theorem nf3or 1837
 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
nf.1 xφ
nf.2 xψ
nf.3 xχ
Assertion
Ref Expression
nf3or x(φ ψ χ)

Proof of Theorem nf3or
StepHypRef Expression
1 df-3or 935 . 2 ((φ ψ χ) ↔ ((φ ψ) χ))
2 nf.1 . . . 4 xφ
3 nf.2 . . . 4 xψ
42, 3nfor 1836 . . 3 x(φ ψ)
5 nf.3 . . 3 xχ
64, 5nfor 1836 . 2 x((φ ψ) χ)
71, 6nfxfr 1570 1 x(φ ψ χ)
 Colors of variables: wff setvar class Syntax hints:   ∨ wo 357   ∨ w3o 933  Ⅎwnf 1544 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-or 359  df-3or 935  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by: (None)
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