Theorem mp3anr3

Description: An inference based on modus ponens. (Contributed by NM, 19-Oct-2007)

	Ref	Expression
Hypotheses	mp3anr3.1	⊢ 𝜃
	mp3anr3.2	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ) → 𝜏 )
Assertion	mp3anr3	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		mp3anr3.1	⊢ 𝜃
2		mp3anr3.2	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ) → 𝜏 )
3	2	ancoms	⊢ ( ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ∧ 𝜑 ) → 𝜏 )
4	1 3	mp3anl3	⊢ ( ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜑 ) → 𝜏 )
5	4	ancoms	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜏 )