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Theorem nfd 1766
 Description: Deduce that x is not free in ψ in a context. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
nfd.1 xφ
nfd.2 (φ → (ψxψ))
Assertion
Ref Expression
nfd (φ → Ⅎxψ)

Proof of Theorem nfd
StepHypRef Expression
1 nfd.1 . . 3 xφ
2 nfd.2 . . 3 (φ → (ψxψ))
31, 2alrimi 1765 . 2 (φx(ψxψ))
4 df-nf 1545 . 2 (Ⅎxψx(ψxψ))
53, 4sylibr 203 1 (φ → Ⅎxψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540  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-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545 This theorem is referenced by:  nfdh  1767  nfnd  1791  nfndOLD  1792  nfald  1852  nfaldOLD  1853  nfeqf  1958  dvelimf  1997  a16nf  2051  nfsb2  2058  sbal2  2134  copsexg  4607
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