Theorem 3syld

Description: Triple syllogism deduction. Deduction associated with 3syld . (Contributed by Jeff Hankins, 4-Aug-2009)

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

Proof

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