Theorem nabi1 31559

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

Assertion

Ref	Expression
nabi1	⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ⊼ 𝜒) ↔ (𝜓 ⊼ 𝜒)))

Proof of Theorem nabi1

Step	Hyp	Ref	Expression
1		nanbi1 1447	1 ⊢ ((𝜑 ↔ 𝜓) → ((𝜑 ⊼ 𝜒) ↔ (𝜓 ⊼ 𝜒)))

Syntax hints:   → wi 4   ↔ wb 195   ⊼ wnan 1439

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 196  df-an 385  df-nan 1440

This theorem is referenced by: (None)