Theorem bicom1

Description: Commutative law for the biconditional. (Contributed by Wolf Lammen, 10-Nov-2012)

	Ref	Expression
Assertion	bicom1	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜓 ↔ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		biimpr	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜓 → 𝜑 ) )
2		biimp	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜑 → 𝜓 ) )
3	1 2	impbid	⊢ ( ( 𝜑 ↔ 𝜓 ) → ( 𝜓 ↔ 𝜑 ) )