Theorem mp3an1

Description: An inference based on modus ponens. (Contributed by NM, 21-Nov-1994)

	Ref	Expression
Hypotheses	mp3an1.1	⊢ 𝜑
	mp3an1.2	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	mp3an1	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		mp3an1.1	⊢ 𝜑
2		mp3an1.2	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
3	2	3expb	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
4	1 3	mpan	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )