Theorem nabi2 32390

Description: Constructor theorem for ⊼. (Contributed by Anthony Hart, 1-Sep-2011.)

Assertion

Ref	Expression
nabi2	⊢ ((𝜑 ↔ 𝜓) → ((𝜒 ⊼ 𝜑) ↔ (𝜒 ⊼ 𝜓)))

Proof of Theorem nabi2

Step	Hyp	Ref	Expression
1		nanbi2 1456	1 ⊢ ((𝜑 ↔ 𝜓) → ((𝜒 ⊼ 𝜑) ↔ (𝜒 ⊼ 𝜓)))

Syntax hints:   → wi 4   ↔ wb 196   ⊼ wnan 1447

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 197  df-an 386  df-nan 1448

This theorem is referenced by: (None)