Theorem pm4.71rd

Description: Deduction converting an implication to a biconditional with conjunction. Deduction from Theorem *4.71 of WhiteheadRussell p. 120. (Contributed by NM, 10-Feb-2005)

	Ref	Expression
Hypothesis	pm4.71rd.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	pm4.71rd	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜒 ∧ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm4.71rd.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
2	1	pm4.71d	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜓 ∧ 𝜒 ) ) )
3	2	biancomd	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜒 ∧ 𝜓 ) ) )