Theorem bicomd

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

	Ref	Expression
Hypothesis	bicomd.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
Assertion	bicomd	$$⊢\phi \to \left(\chi \leftrightarrow \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bicomd.1	$$⊢\phi \to \left(\psi \leftrightarrow \chi \right)$$
2		bicom	$$⊢\left(\psi \leftrightarrow \chi \right)\leftrightarrow \left(\chi \leftrightarrow \psi \right)$$
3	1 2	sylib	$$⊢\phi \to \left(\chi \leftrightarrow \psi \right)$$