Theorem mpan2d

Description: A deduction based on modus ponens. (Contributed by NM, 12-Dec-2004)

	Ref	Expression
Hypotheses	mpan2d.1	⊢ ( 𝜑 → 𝜒 )
	mpan2d.2	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) )
Assertion	mpan2d	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		mpan2d.1	⊢ ( 𝜑 → 𝜒 )
2		mpan2d.2	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) )
3	2	expd	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
4	1 3	mpid	⊢ ( 𝜑 → ( 𝜓 → 𝜃 ) )