Theorem 19.20dvv 948

Description: Deduction from Theorem 19.22 of [Margaris] p. 90.

Hypothesis

Ref	Expression
19.20dvv.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
19.20dvv	⊢ (φ → (∀x∀yψ → ∀x∀yχ))

Distinct variable group(s):   φ,x   φ,y

Proof of Theorem 19.20dvv

Step	Hyp	Ref	Expression
1		19.20dvv.1	. . 3 ⊢ (φ → (ψ → χ))
2	1	19.20dv 946	. 2 ⊢ (φ → (∀yψ → ∀yχ))
3	2	19.20dv 946	1 ⊢ (φ → (∀x∀yψ → ∀x∀yχ))

Syntax hints:   → wi 2  ∀wal 672

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677  ax-17 925

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