Theorem nabi12i

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

	Ref	Expression
Hypotheses	nabi12i.1	⊢ ( 𝜑 ↔ 𝜓 )
	nabi12i.2	⊢ ( 𝜒 ↔ 𝜃 )
	nabi12i.3	⊢ ( 𝜓 ⊼ 𝜃 )
Assertion	nabi12i	⊢ ( 𝜑 ⊼ 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		nabi12i.1	⊢ ( 𝜑 ↔ 𝜓 )
2		nabi12i.2	⊢ ( 𝜒 ↔ 𝜃 )
3		nabi12i.3	⊢ ( 𝜓 ⊼ 𝜃 )
4	1 3	nabi1i	⊢ ( 𝜑 ⊼ 𝜃 )
5	2 4	nabi2i	⊢ ( 𝜑 ⊼ 𝜒 )