This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

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	⊢ ( ( 𝜑 → ( 𝜑 → 𝜓 ) ) → ( 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		pm2.27	⊢ ( 𝜑 → ( ( 𝜑 → 𝜓 ) → 𝜓 ) )
2	1	a2i	⊢ ( ( 𝜑 → ( 𝜑 → 𝜓 ) ) → ( 𝜑 → 𝜓 ) )