Theorem mp3an1i

Description: An inference based on modus ponens. (Contributed by NM, 5-Jul-2005)

	Ref	Expression
Hypotheses	mp3an1i.1	⊢ 𝜓
	mp3an1i.2	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜏 ) )
Assertion	mp3an1i	⊢ ( 𝜑 → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) )

Proof

Step	Hyp	Ref	Expression
1		mp3an1i.1	⊢ 𝜓
2		mp3an1i.2	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜏 ) )
3	2	com12	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → ( 𝜑 → 𝜏 ) )
4	1 3	mp3an1	⊢ ( ( 𝜒 ∧ 𝜃 ) → ( 𝜑 → 𝜏 ) )
5	4	com12	⊢ ( 𝜑 → ( ( 𝜒 ∧ 𝜃 ) → 𝜏 ) )