Theorem alrimdv 1633

Description: Deduction from Theorem 19.21 of [Margaris] p. 90. (Contributed by NM, 10-Feb-1997.)

Hypothesis

Ref	Expression
alrimdv.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
alrimdv	⊢ (φ → (ψ → ∀xχ))

Distinct variable groups:   φ,x   ψ,x

Allowed substitution hint:   χ(x)

Proof of Theorem alrimdv

Step	Hyp	Ref	Expression
1		ax-17 1616	. 2 ⊢ (φ → ∀xφ)
2		ax-17 1616	. 2 ⊢ (ψ → ∀xψ)
3		alrimdv.1	. 2 ⊢ (φ → (ψ → χ))
4	1, 2, 3	alrimdh 1587	1 ⊢ (φ → (ψ → ∀xχ))

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1546  ax-5 1557  ax-17 1616

This theorem is referenced by:  funcnvuni  5162  eqfnfv  5393