Theorem syldd 50

Description: Nested syllogism deduction.

Hypotheses

Ref	Expression
syldd.1	⊢ (φ → (ψ → (χ → θ)))
syldd.2	⊢ (φ → (ψ → (θ → τ)))

Assertion

Ref	Expression
syldd	⊢ (φ → (ψ → (χ → τ)))

Proof of Theorem syldd

Step	Hyp	Ref	Expression
1		syldd.1	. 2 ⊢ (φ → (ψ → (χ → θ)))
2		syldd.2	. . 3 ⊢ (φ → (ψ → (θ → τ)))
3		syl1 16	. . 3 ⊢ ((θ → τ) → ((χ → θ) → (χ → τ)))
4	2, 3	syl6 23	. 2 ⊢ (φ → (ψ → ((χ → θ) → (χ → τ))))
5	1, 4	mpdd 47	1 ⊢ (φ → (ψ → (χ → τ)))

Syntax hints:   → wi 2

This theorem is referenced by:  prlem934 3933

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

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