Theorem syl5com

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

	Ref	Expression
Hypotheses	syl5com.1	$$⊢\phi \to \psi$$
	syl5com.2	$$⊢\chi \to \left(\psi \to \theta \right)$$
Assertion	syl5com	$$⊢\phi \to \left(\chi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		syl5com.1	$$⊢\phi \to \psi$$
2		syl5com.2	$$⊢\chi \to \left(\psi \to \theta \right)$$
3	1	a1d	$$⊢\phi \to \left(\chi \to \psi \right)$$
4	3 2	sylcom	$$⊢\phi \to \left(\chi \to \theta \right)$$