Theorem nfrd 1410

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 1408	. 2 ⊢ (Ⅎxψ → (ψ → ∀xψ))
3	1, 2	syl 14	1 ⊢ (φ → (ψ → ∀xψ))

Syntax hints:   → wi 4  ∀wal 1240  Ⅎwnf 1346

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-4 1397

This theorem depends on definitions:  df-bi 110  df-nf 1347

This theorem is referenced by:  nfan1  1453  nfim1  1460  alrimdd  1497  spimed  1625  cbv2  1632  nfald  1640  sbied  1668  cbvexd  1799  sbcomxyyz  1843  hbsbd  1855  dvelimALT  1883  dvelimfv  1884  hbeud  1919  abidnf  2703  eusvnfb  4152