Theorem mp3an13

Description: An inference based on modus ponens. (Contributed by NM, 14-Jul-2005)

	Ref	Expression
Hypotheses	mp3an13.1	⊢ 𝜑
	mp3an13.2	⊢ 𝜒
	mp3an13.3	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	mp3an13	⊢ ( 𝜓 → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		mp3an13.1	⊢ 𝜑
2		mp3an13.2	⊢ 𝜒
3		mp3an13.3	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
4	2 3	mp3an3	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )
5	1 4	mpan	⊢ ( 𝜓 → 𝜃 )