Theorem nfrd 1763

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 1761	. 2 ⊢ (Ⅎxψ → (ψ → ∀xψ))
3	1, 2	syl 15	1 ⊢ (φ → (ψ → ∀xψ))

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:  alrimdd  1768  nfim1  1811  nfim1OLD  1812  hbimd  1815  nfald  1852  19.9tOLD  1857  19.21tOLD  1863  nfan1  1881  cbv1  1979  cbv2  1981  sbied  2036  sbal1  2126  abidnf  3006