Theorem nabi1i

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

	Ref	Expression
Hypotheses	nabi1i.1	⊢ ( 𝜑 ↔ 𝜓 )
	nabi1i.2	⊢ ( 𝜓 ⊼ 𝜒 )
Assertion	nabi1i	⊢ ( 𝜑 ⊼ 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		nabi1i.1	⊢ ( 𝜑 ↔ 𝜓 )
2		nabi1i.2	⊢ ( 𝜓 ⊼ 𝜒 )
3	1	bicomi	⊢ ( 𝜓 ↔ 𝜑 )
4	3	nanbi1i	⊢ ( ( 𝜓 ⊼ 𝜒 ) ↔ ( 𝜑 ⊼ 𝜒 ) )
5	2 4	mpbi	⊢ ( 𝜑 ⊼ 𝜒 )