Theorem mp3an3

Description: An inference based on modus ponens. (Contributed by NM, 21-Nov-1994)

	Ref	Expression
Hypotheses	mp3an3.1	⊢ 𝜒
	mp3an3.2	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	mp3an3	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		mp3an3.1	⊢ 𝜒
2		mp3an3.2	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
3	2	3expia	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 → 𝜃 ) )
4	1 3	mpi	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )