Theorem bicomd

Description: Commute two sides of a biconditional in a deduction. (Contributed by NM, 14-May-1993)

	Ref	Expression
Hypothesis	bicomd.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
Assertion	bicomd	⊢ ( 𝜑 → ( 𝜒 ↔ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		bicomd.1	⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) )
2		bicom	⊢ ( ( 𝜓 ↔ 𝜒 ) ↔ ( 𝜒 ↔ 𝜓 ) )
3	1 2	sylib	⊢ ( 𝜑 → ( 𝜒 ↔ 𝜓 ) )