Theorem syl5com

Description: Syllogism inference with commuted antecedents. (Contributed by NM, 24-May-2005)

	Ref	Expression
Hypotheses	syl5com.1	⊢ ( 𝜑 → 𝜓 )
	syl5com.2	⊢ ( 𝜒 → ( 𝜓 → 𝜃 ) )
Assertion	syl5com	⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		syl5com.1	⊢ ( 𝜑 → 𝜓 )
2		syl5com.2	⊢ ( 𝜒 → ( 𝜓 → 𝜃 ) )
3	1	a1d	⊢ ( 𝜑 → ( 𝜒 → 𝜓 ) )
4	3 2	sylcom	⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )