Theorem mpanlr1

Description: An inference based on modus ponens. (Contributed by NM, 30-Dec-2004) (Proof shortened by Wolf Lammen, 7-Apr-2013)

	Ref	Expression
Hypotheses	mpanlr1.1	⊢ 𝜓
	mpanlr1.2	⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) ∧ 𝜃 ) → 𝜏 )
Assertion	mpanlr1	⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		mpanlr1.1	⊢ 𝜓
2		mpanlr1.2	⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) ∧ 𝜃 ) → 𝜏 )
3	1	jctl	⊢ ( 𝜒 → ( 𝜓 ∧ 𝜒 ) )
4	3 2	sylanl2	⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )