Theorem mp3an23

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

	Ref	Expression
Hypotheses	mp3an23.1	⊢ 𝜓
	mp3an23.2	⊢ 𝜒
	mp3an23.3	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	mp3an23	⊢ ( 𝜑 → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		mp3an23.1	⊢ 𝜓
2		mp3an23.2	⊢ 𝜒
3		mp3an23.3	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
4	2 3	mp3an3	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )
5	1 4	mpan2	⊢ ( 𝜑 → 𝜃 )