Theorem mp2ani

Description: An inference based on modus ponens. (Contributed by NM, 12-Dec-2004)

	Ref	Expression
Hypotheses	mp2ani.1	⊢ 𝜓
	mp2ani.2	⊢ 𝜒
	mp2ani.3	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) )
Assertion	mp2ani	⊢ ( 𝜑 → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		mp2ani.1	⊢ 𝜓
2		mp2ani.2	⊢ 𝜒
3		mp2ani.3	⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) → 𝜃 ) )
4	1 3	mpani	⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )
5	2 4	mpi	⊢ ( 𝜑 → 𝜃 )