Theorem syl11

Description: A syllogism inference. Commuted form of an instance of syl . (Contributed by BJ, 25-Oct-2021)

	Ref	Expression
Hypotheses	syl11.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	syl11.2	⊢ ( 𝜃 → 𝜑 )
Assertion	syl11	⊢ ( 𝜓 → ( 𝜃 → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		syl11.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2		syl11.2	⊢ ( 𝜃 → 𝜑 )
3	2 1	syl	⊢ ( 𝜃 → ( 𝜓 → 𝜒 ) )
4	3	com12	⊢ ( 𝜓 → ( 𝜃 → 𝜒 ) )