Theorem nanbi2i

Description: Introduce a left anti-conjunct to both sides of a logical equivalence. (Contributed by SF, 2-Jan-2018)

	Ref	Expression
Hypothesis	nanbii.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	nanbi2i	$$⊢\left(\chi ⊼\phi \right)\leftrightarrow \left(\chi ⊼\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nanbii.1	$$⊢\phi \leftrightarrow \psi$$
2		nanbi2	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\left(\chi ⊼\phi \right)\leftrightarrow \left(\chi ⊼\psi \right)\right)$$
3	1 2	ax-mp	$$⊢\left(\chi ⊼\phi \right)\leftrightarrow \left(\chi ⊼\psi \right)$$