Theorem nabi1i

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

	Ref	Expression
Hypotheses	nabi1i.1	$$⊢\phi \leftrightarrow \psi$$
	nabi1i.2	$$⊢\left(\psi ⊼\chi \right)$$
Assertion	nabi1i	$$⊢\left(\phi ⊼\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nabi1i.1	$$⊢\phi \leftrightarrow \psi$$
2		nabi1i.2	$$⊢\left(\psi ⊼\chi \right)$$
3	1	bicomi	$$⊢\psi \leftrightarrow \phi$$
4	3	nanbi1i	$$⊢\left(\psi ⊼\chi \right)\leftrightarrow \left(\phi ⊼\chi \right)$$
5	2 4	mpbi	$$⊢\left(\phi ⊼\chi \right)$$