Theorem bi2.04

Description: Logical equivalence of commuted antecedents. Part of Theorem *4.87 of WhiteheadRussell p. 122. (Contributed by NM, 11-May-1993)

	Ref	Expression
Assertion	bi2.04	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\leftrightarrow \left(\psi \to \left(\phi \to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm2.04	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\psi \to \left(\phi \to \chi \right)\right)$$
2		pm2.04	$$⊢\left(\psi \to \left(\phi \to \chi \right)\right)\to \left(\phi \to \left(\psi \to \chi \right)\right)$$
3	1 2	impbii	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\leftrightarrow \left(\psi \to \left(\phi \to \chi \right)\right)$$