Theorem mp3an12

Description: An inference based on modus ponens. (Contributed by NM, 13-Jul-2005)

	Ref	Expression
Hypotheses	mp3an12.1	⊢ 𝜑
	mp3an12.2	⊢ 𝜓
	mp3an12.3	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	mp3an12	⊢ ( 𝜒 → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		mp3an12.1	⊢ 𝜑
2		mp3an12.2	⊢ 𝜓
3		mp3an12.3	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
4	1 3	mp3an1	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
5	2 4	mpan	⊢ ( 𝜒 → 𝜃 )