Theorem 2alimdv 1623

Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 27-Apr-2004.)

Hypothesis

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

Assertion

Ref	Expression
2alimdv	⊢ (φ → (∀x∀yψ → ∀x∀yχ))

Distinct variable groups:   φ,x   φ,y

Allowed substitution hints:   ψ(x,y)   χ(x,y)

Proof of Theorem 2alimdv

Step	Hyp	Ref	Expression
1		2alimdv.1	. . 3 ⊢ (φ → (ψ → χ))
2	1	alimdv 1621	. 2 ⊢ (φ → (∀yψ → ∀yχ))
3	2	alimdv 1621	1 ⊢ (φ → (∀x∀yψ → ∀x∀yχ))

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: (None)