Theorem 3syld 51

Description: Triple syllogism deduction. (Contributed by Jeff Hankins, 4-Aug-2009.)

Hypotheses

Ref	Expression
3syld.1	⊢ (φ → (ψ → χ))
3syld.2	⊢ (φ → (χ → θ))
3syld.3	⊢ (φ → (θ → τ))

Assertion

Ref	Expression
3syld	⊢ (φ → (ψ → τ))

Proof of Theorem 3syld

Step	Hyp	Ref	Expression
1		3syld.1	. . 3 ⊢ (φ → (ψ → χ))
2		3syld.2	. . 3 ⊢ (φ → (χ → θ))
3	1, 2	syld 40	. 2 ⊢ (φ → (ψ → θ))
4		3syld.3	. 2 ⊢ (φ → (θ → τ))
5	3, 4	syld 40	1 ⊢ (φ → (ψ → τ))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  nchoicelem17  6306