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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  wnf 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-or 359  df-3or 935  df-tru 1319  df-ex 1542  df-nf 1545
This theorem is referenced by: (None)
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