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	⊢ ( 𝜓 → 𝜑 )
	mpcom.2	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	mpcom	⊢ ( 𝜓 → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		mpcom.1	⊢ ( 𝜓 → 𝜑 )
2		mpcom.2	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
3	2	com12	⊢ ( 𝜓 → ( 𝜑 → 𝜒 ) )
4	1 3	mpd	⊢ ( 𝜓 → 𝜒 )