Theorem syl6com

Description: Syllogism inference with commuted antecedents. (Contributed by NM, 25-May-2005)

	Ref	Expression
Hypotheses	syl6com.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	syl6com.2	⊢ ( 𝜒 → 𝜃 )
Assertion	syl6com	⊢ ( 𝜓 → ( 𝜑 → 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		syl6com.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		syl6com.2	⊢ ( 𝜒 → 𝜃 )
3	1 2	syl6	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )
4	3	com12	⊢ ( 𝜓 → ( 𝜑 → 𝜃 ) )