Theorem syldc

Description: Syllogism deduction. Commuted form of syld . (Contributed by BJ, 25-Oct-2021)

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

Proof

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