Theorem pm2.43

Description: Absorption of redundant antecedent. Also called the "Contraction" or "Hilbert" axiom. Theorem *2.43 of WhiteheadRussell p. 106. (Contributed by NM, 10-Jan-1993) (Proof shortened by Mel L. O'Cat, 15-Aug-2004)

	Ref	Expression
Assertion	pm2.43	$$⊢\left(\phi \to \left(\phi \to \psi \right)\right)\to \left(\phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		pm2.27	$$⊢\phi \to \left(\left(\phi \to \psi \right)\to \psi \right)$$
2	1	a2i	$$⊢\left(\phi \to \left(\phi \to \psi \right)\right)\to \left(\phi \to \psi \right)$$