Theorem naim2i

Description: Constructor rule for -/\ . (Contributed by Anthony Hart, 2-Sep-2011)

	Ref	Expression
Hypotheses	naim2i.1	⊢ ( 𝜑 → 𝜓 )
	naim2i.2	⊢ ( 𝜒 ⊼ 𝜓 )
Assertion	naim2i	⊢ ( 𝜒 ⊼ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		naim2i.1	⊢ ( 𝜑 → 𝜓 )
2		naim2i.2	⊢ ( 𝜒 ⊼ 𝜓 )
3		naim2	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜒 ⊼ 𝜓 ) → ( 𝜒 ⊼ 𝜑 ) ) )
4	1 2 3	mp2	⊢ ( 𝜒 ⊼ 𝜑 )