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Theorem hb3an 1830
 Description: If x is not free in φ, ψ, and χ, it is not free in (φ ∧ ψ ∧ χ). (Contributed by NM, 14-Sep-2003.) (Proof shortened by Wolf Lammen, 2-Jan-2018.)
Hypotheses
Ref Expression
hb.1 (φxφ)
hb.2 (ψxψ)
hb.3 (χxχ)
Assertion
Ref Expression
hb3an ((φ ψ χ) → x(φ ψ χ))

Proof of Theorem hb3an
StepHypRef Expression
1 hb.1 . . . 4 (φxφ)
21nfi 1551 . . 3 xφ
3 hb.2 . . . 4 (ψxψ)
43nfi 1551 . . 3 xψ
5 hb.3 . . . 4 (χxχ)
65nfi 1551 . . 3 xχ
72, 4, 6nf3an 1827 . 2 x(φ ψ χ)
87nfri 1762 1 ((φ ψ χ) → x(φ ψ χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 934  ∀wal 1540 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: (None)
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