Theorem pm5.1

Description: Two propositions are equivalent if they are both true. Theorem *5.1 of WhiteheadRussell p. 123. (Contributed by NM, 21-May-1994)

	Ref	Expression
Assertion	pm5.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.501	⊢ ( 𝜑 → ( 𝜓 ↔ ( 𝜑 ↔ 𝜓 ) ) )
2	1	biimpa	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) )