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Theorem nf3or 1976
Description: If 𝑥 is not free in 𝜑, 𝜓, and 𝜒, it is not free in (𝜑𝜓𝜒). (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypotheses
Ref Expression
nf.1 𝑥𝜑
nf.2 𝑥𝜓
nf.3 𝑥𝜒
Assertion
Ref Expression
nf3or 𝑥(𝜑𝜓𝜒)

Proof of Theorem nf3or
StepHypRef Expression
1 df-3or 1073 . 2 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∨ 𝜒))
2 nf.1 . . . 4 𝑥𝜑
3 nf.2 . . . 4 𝑥𝜓
42, 3nfor 1975 . . 3 𝑥(𝜑𝜓)
5 nf.3 . . 3 𝑥𝜒
64, 5nfor 1975 . 2 𝑥((𝜑𝜓) ∨ 𝜒)
71, 6nfxfr 1920 1 𝑥(𝜑𝜓𝜒)
Colors of variables: wff setvar class
Syntax hints:  wo 382  w3o 1071  wnf 1849
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1863  ax-4 1878
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3or 1073  df-ex 1846  df-nf 1851
This theorem is referenced by:  nfso  5185
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