Theorem nanbi1i

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

	Ref	Expression
Hypothesis	nanbii.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	nanbi1i	$$⊢\left(\phi ⊼\chi \right)\leftrightarrow \left(\psi ⊼\chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nanbii.1	$$⊢\phi \leftrightarrow \psi$$
2		nanbi1	$$⊢\left(\phi \leftrightarrow \psi \right)\to \left(\left(\phi ⊼\chi \right)\leftrightarrow \left(\psi ⊼\chi \right)\right)$$
3	1 2	ax-mp	$$⊢\left(\phi ⊼\chi \right)\leftrightarrow \left(\psi ⊼\chi \right)$$