Theorem nabi2i

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

	Ref	Expression
Hypotheses	nabi2i.1	⊢ ( 𝜑 ↔ 𝜓 )
	nabi2i.2	⊢ ( 𝜒 ⊼ 𝜓 )
Assertion	nabi2i	⊢ ( 𝜒 ⊼ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		nabi2i.1	⊢ ( 𝜑 ↔ 𝜓 )
2		nabi2i.2	⊢ ( 𝜒 ⊼ 𝜓 )
3	1	bicomi	⊢ ( 𝜓 ↔ 𝜑 )
4	3	nanbi2i	⊢ ( ( 𝜒 ⊼ 𝜓 ) ↔ ( 𝜒 ⊼ 𝜑 ) )
5	2 4	mpbi	⊢ ( 𝜒 ⊼ 𝜑 )