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	⊢ ( 𝜑 ↔ 𝜓 )
Assertion	nanbi2i	⊢ ( ( 𝜒 ⊼ 𝜑 ) ↔ ( 𝜒 ⊼ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		nanbii.1	⊢ ( 𝜑 ↔ 𝜓 )
2		nanbi2	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( ( 𝜒 ⊼ 𝜑 ) ↔ ( 𝜒 ⊼ 𝜓 ) ) )
3	1 2	ax-mp	⊢ ( ( 𝜒 ⊼ 𝜑 ) ↔ ( 𝜒 ⊼ 𝜓 ) )