Theorem pm2.04

Description: Swap antecedents. Theorem *2.04 of WhiteheadRussell p. 100. This was the third axiom in Frege's logic system, specifically Proposition 8 of Frege1879 p. 35. Its associated inference is com12 . (Contributed by NM, 27-Dec-1992) (Proof shortened by Wolf Lammen, 12-Sep-2012)

	Ref	Expression
Assertion	pm2.04	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\psi \to \left(\phi \to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\phi \to \left(\psi \to \chi \right)\right)$$
2	1	com23	$$⊢\left(\phi \to \left(\psi \to \chi \right)\right)\to \left(\psi \to \left(\phi \to \chi \right)\right)$$