Theorem syl6com

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

	Ref	Expression
Hypotheses	syl6com.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	syl6com.2	$$⊢\chi \to \theta$$
Assertion	syl6com	$$⊢\psi \to \left(\phi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		syl6com.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		syl6com.2	$$⊢\chi \to \theta$$
3	1 2	syl6	$$⊢\phi \to \left(\psi \to \theta \right)$$
4	3	com12	$$⊢\psi \to \left(\phi \to \theta \right)$$