Theorem sylanr2

Description: A syllogism inference. (Contributed by NM, 9-Apr-2005)

	Ref	Expression
Hypotheses	sylanr2.1	⊢ ( 𝜑 → 𝜃 )
	sylanr2.2	⊢ ( ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) → 𝜏 )
Assertion	sylanr2	⊢ ( ( 𝜓 ∧ ( 𝜒 ∧ 𝜑 ) ) → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		sylanr2.1	⊢ ( 𝜑 → 𝜃 )
2		sylanr2.2	⊢ ( ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) → 𝜏 )
3	1	anim2i	⊢ ( ( 𝜒 ∧ 𝜑 ) → ( 𝜒 ∧ 𝜃 ) )
4	3 2	sylan2	⊢ ( ( 𝜓 ∧ ( 𝜒 ∧ 𝜑 ) ) → 𝜏 )