Theorem mpanr1

Description: An inference based on modus ponens. (Contributed by NM, 3-May-1994) (Proof shortened by Andrew Salmon, 7-May-2011)

	Ref	Expression
Hypotheses	mpanr1.1	⊢ 𝜓
	mpanr1.2	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
Assertion	mpanr1	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		mpanr1.1	⊢ 𝜓
2		mpanr1.2	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
3	2	anassrs	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
4	1 3	mpanl2	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )