Theorem mpcom

Description: Modus ponens inference with commutation of antecedents. Commuted form of mpd . (Contributed by NM, 17-Mar-1996)

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

Proof

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