Theorem mp3an

Description: An inference based on modus ponens. (Contributed by NM, 14-May-1999)

	Ref	Expression
Hypotheses	mp3an.1	⊢ 𝜑
	mp3an.2	⊢ 𝜓
	mp3an.3	⊢ 𝜒
	mp3an.4	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	mp3an	⊢ 𝜃

Proof

Step	Hyp	Ref	Expression
1		mp3an.1	⊢ 𝜑
2		mp3an.2	⊢ 𝜓
3		mp3an.3	⊢ 𝜒
4		mp3an.4	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
5	1 4	mp3an1	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
6	2 3 5	mp2an	⊢ 𝜃