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Metamath Proof Explorer

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	\|- ( ( ph -> ( ph -> ps ) ) -> ( ph -> ps ) )

Proof

Step	Hyp	Ref	Expression
1		pm2.27	\|- ( ph -> ( ( ph -> ps ) -> ps ) )
2	1	a2i	\|- ( ( ph -> ( ph -> ps ) ) -> ( ph -> ps ) )