Theorem pm4.71ri

Description: Inference converting an implication to a biconditional with conjunction. Inference from Theorem *4.71 of WhiteheadRussell p. 120 (with conjunct reversed). (Contributed by NM, 1-Dec-2003)

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

Proof

Step	Hyp	Ref	Expression
1		pm4.71ri.1	⊢ ( 𝜑 → 𝜓 )
2	1	pm4.71i	⊢ ( 𝜑 ↔ ( 𝜑 ∧ 𝜓 ) )
3	2	biancomi	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜑 ) )