Theorem mpanl1

Description: An inference based on modus ponens. (Contributed by NM, 16-Aug-1994) (Proof shortened by Wolf Lammen, 7-Apr-2013)

	Ref	Expression
Hypotheses	mpanl1.1	⊢ 𝜑
	mpanl1.2	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
Assertion	mpanl1	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		mpanl1.1	⊢ 𝜑
2		mpanl1.2	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
3	1	jctl	⊢ ( 𝜓 → ( 𝜑 ∧ 𝜓 ) )
4	3 2	sylan	⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )