Theorem nanbi1i 1500

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

Hypothesis

Ref	Expression
nanbii.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
nanbi1i	⊢ ((𝜑 ⊼ 𝜒) ↔ (𝜓 ⊼ 𝜒))

Proof of Theorem nanbi1i

Step	Hyp	Ref	Expression
1		nanbii.1	. 2 ⊢ (𝜑 ↔ 𝜓)
2		nanbi1 1497	. 2 ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ⊼ 𝜒) ↔ (𝜓 ⊼ 𝜒)))
3	1, 2	ax-mp 5	1 ⊢ ((𝜑 ⊼ 𝜒) ↔ (𝜓 ⊼ 𝜒))

Syntax hints:   ↔ wb 209   ⊼ wnan 1487

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 210  df-an 400  df-nan 1488

This theorem is referenced by:  nabi1i  34485