Theorem mpanl2

Description: An inference based on modus ponens. (Contributed by NM, 16-Aug-1994) (Proof shortened by Andrew Salmon, 7-May-2011)

	Ref	Expression
Hypotheses	mpanl2.1	⊢ 𝜓
	mpanl2.2	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
Assertion	mpanl2	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		mpanl2.1	⊢ 𝜓
2		mpanl2.2	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
3	1	jctr	⊢ ( 𝜑 → ( 𝜑 ∧ 𝜓 ) )
4	3 2	sylan	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )