Theorem mp3anl2

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

	Ref	Expression
Hypotheses	mp3anl2.1	⊢ 𝜓
	mp3anl2.2	⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )
Assertion	mp3anl2	⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		mp3anl2.1	⊢ 𝜓
2		mp3anl2.2	⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )
3	2	ex	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ( 𝜃 → 𝜏 ) )
4	1 3	mp3an2	⊢ ( ( 𝜑 ∧ 𝜒 ) → ( 𝜃 → 𝜏 ) )
5	4	imp	⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )