Theorem syl6c

Description: Inference combining syl6 with contraction. (Contributed by Alan Sare, 2-May-2011)

	Ref	Expression
Hypotheses	syl6c.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	syl6c.2	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
	syl6c.3	⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
Assertion	syl6c	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )

Proof

Step	Hyp	Ref	Expression
1		syl6c.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		syl6c.2	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
3		syl6c.3	⊢ ( 𝜒 → ( 𝜃 → 𝜏 ) )
4	1 3	syl6	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜏 ) ) )
5	2 4	mpdd	⊢ ( 𝜑 → ( 𝜓 → 𝜏 ) )