Theorem bicom

Description: Commutative law for the biconditional. Theorem *4.21 of WhiteheadRussell p. 117. (Contributed by NM, 11-May-1993)

	Ref	Expression
Assertion	bicom	⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ( 𝜓 ↔ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		bicom1	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜓 ↔ 𝜑 ) )
2		bicom1	⊢ ( ( 𝜓 ↔ 𝜑 ) → ( 𝜑 ↔ 𝜓 ) )
3	1 2	impbii	⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ( 𝜓 ↔ 𝜑 ) )