Theorem syl56

Description: Combine syl5 and syl6 . (Contributed by NM, 14-Nov-2013)

	Ref	Expression
Hypotheses	syl56.1	⊢ ( 𝜑 → 𝜓 )
	syl56.2	⊢ ( 𝜒 → ( 𝜓 → 𝜃 ) )
	syl56.3	⊢ ( 𝜃 → 𝜏 )
Assertion	syl56	⊢ ( 𝜒 → ( 𝜑 → 𝜏 ) )

Proof

Step	Hyp	Ref	Expression
1		syl56.1	⊢ ( 𝜑 → 𝜓 )
2		syl56.2	⊢ ( 𝜒 → ( 𝜓 → 𝜃 ) )
3		syl56.3	⊢ ( 𝜃 → 𝜏 )
4	2 3	syl6	⊢ ( 𝜒 → ( 𝜓 → 𝜏 ) )
5	1 4	syl5	⊢ ( 𝜒 → ( 𝜑 → 𝜏 ) )