Theorem nic-bijust

Description: Biconditional justification from Nicod's axiom. For nic-* definitions, the biconditional connective is not used. Instead, definitions are made based on this form. nic-bi1 and nic-bi2 are used to convert the definitions into usable theorems about one side of the implication. (Contributed by Jeff Hoffman, 18-Nov-2007) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	nic-bijust	⊢ ( ( 𝜏 ⊼ 𝜏 ) ⊼ ( ( 𝜏 ⊼ 𝜏 ) ⊼ ( 𝜏 ⊼ 𝜏 ) ) )

Proof

Step	Hyp	Ref	Expression
1		nic-swap	⊢ ( ( 𝜏 ⊼ 𝜏 ) ⊼ ( ( 𝜏 ⊼ 𝜏 ) ⊼ ( 𝜏 ⊼ 𝜏 ) ) )