Theorem a4sd 683

Description: Deduction generalizing antecedent.

Hypothesis

Ref	Expression
a4sd.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
a4sd	⊢ (φ → (∀xψ → χ))

Proof of Theorem a4sd

Step	Hyp	Ref	Expression
1		a4sd.1	. 2 ⊢ (φ → (ψ → χ))
2		ax-4 673	. 2 ⊢ (∀xψ → ψ)
3	1, 2	syl5 22	1 ⊢ (φ → (∀xψ → χ))

Syntax hints:   → wi 2  ∀wal 672

This theorem is referenced by:  moexex 1058  zornlem4 3606  zornlem5 3607  axpowndlem3 3745  axacndlem5 3757  suppsr3 4018

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-mp 6  ax-4 673

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