Theorem naim1i

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

	Ref	Expression
Hypotheses	naim1i.1	⊢ ( 𝜑 → 𝜓 )
	naim1i.2	⊢ ( 𝜓 ⊼ 𝜒 )
Assertion	naim1i	⊢ ( 𝜑 ⊼ 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		naim1i.1	⊢ ( 𝜑 → 𝜓 )
2		naim1i.2	⊢ ( 𝜓 ⊼ 𝜒 )
3		naim1	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜓 ⊼ 𝜒 ) → ( 𝜑 ⊼ 𝜒 ) ) )
4	1 2 3	mp2	⊢ ( 𝜑 ⊼ 𝜒 )