Theorem alimd 1764

Description: Deduction from Theorem 19.20 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

Ref	Expression
alimd.1	⊢ Ⅎxφ
alimd.2	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
alimd	⊢ (φ → (∀xψ → ∀xχ))

Proof of Theorem alimd

Step	Hyp	Ref	Expression
1		alimd.1	. . 3 ⊢ Ⅎxφ
2	1	nfri 1762	. 2 ⊢ (φ → ∀xφ)
3		alimd.2	. 2 ⊢ (φ → (ψ → χ))
4	2, 3	alimdh 1563	1 ⊢ (φ → (∀xψ → ∀xχ))

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  nfimdOLD  1809  spimt  1974  sbied  2036  sb9i  2094  mo  2226  2mo  2282  ralimdaa  2692