Theorem pm3.35

Description: Conjunctive detachment. Theorem *3.35 of WhiteheadRussell p. 112. Variant of pm2.27 . (Contributed by NM, 14-Dec-2002)

	Ref	Expression
Assertion	pm3.35	⊢ ( ( 𝜑 ∧ ( 𝜑 → 𝜓 ) ) → 𝜓 )

Proof

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