Theorem nfrd 1390

Description: Consequence of the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypothesis

Ref	Expression
nfrd.1	⊢ (φ → Ⅎxψ)

Assertion

Ref	Expression
nfrd	⊢ (φ → (ψ → ∀xψ))

Proof of Theorem nfrd

Step	Hyp	Ref	Expression
1		nfrd.1	. 2 ⊢ (φ → Ⅎxψ)
2		nfr 1388	. 2 ⊢ (Ⅎxψ → (ψ → ∀xψ))
3	1, 2	syl 14	1 ⊢ (φ → (ψ → ∀xψ))

Syntax hints:   → wi 4  ∀wal 1224  Ⅎwnf 1325

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-4 1377

This theorem depends on definitions:  df-bi 110  df-nf 1326

This theorem is referenced by:  nfan1  1434  nfim1  1441  alrimdd  1478  spimed  1606  cbv2  1613  nfald  1621  sbied  1649  cbvexd  1780  sbcomxyyz  1824  hbsbd  1836  dvelimALT  1864  dvelimfv  1865  hbeud  1900  abidnf  2682  eusvnfb  4132