Theorem syl5d 53

Description: A nested syllogism deduction. (The proof was shortened by Josh Purinton, 29-Dec-00.)

Hypotheses

Ref	Expression
syl5d.1	⊢ (φ → (ψ → (χ → θ)))
syl5d.2	⊢ (φ → (τ → χ))

Assertion

Ref	Expression
syl5d	⊢ (φ → (ψ → (τ → θ)))

Proof of Theorem syl5d

Step	Hyp	Ref	Expression
1		syl5d.1	. 2 ⊢ (φ → (ψ → (χ → θ)))
2		syl5d.2	. . 3 ⊢ (φ → (τ → χ))
3	2	syl4d 28	. 2 ⊢ (φ → ((χ → θ) → (τ → θ)))
4	1, 3	syld 27	1 ⊢ (φ → (ψ → (τ → θ)))

Syntax hints:   → wi 2

This theorem is referenced by:  syl9 55  sbi1 884  isofrlem 2939  nnmordi 3188  kmlem8 3587  sqrlem6 4736

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

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