Theorem mp3anl1

Description: An inference based on modus ponens. (Contributed by NM, 24-Feb-2005)

	Ref	Expression
Hypotheses	mp3anl1.1	⊢ 𝜑
	mp3anl1.2	⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )
Assertion	mp3anl1	⊢ ( ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		mp3anl1.1	⊢ 𝜑
2		mp3anl1.2	⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )
3	2	ex	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ( 𝜃 → 𝜏 ) )
4	1 3	mp3an1	⊢ ( ( 𝜓 ∧ 𝜒 ) → ( 𝜃 → 𝜏 ) )
5	4	imp	⊢ ( ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )