Theorem bicom1 223

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

Assertion

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

Proof of Theorem bicom1

Step	Hyp	Ref	Expression
1		biimpr 222	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜓 → 𝜑))
2		biimp 217	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 → 𝜓))
3	1, 2	impbid 214	1 ⊢ ((𝜑 ↔ 𝜓) → (𝜓 ↔ 𝜑))

Syntax hints:   → wi 4   ↔ wb 208

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 209

This theorem is referenced by:  bicom  224  bicomi  226  con3ALTOLD  1081  nanass  1499  frege55aid  40204  frege55lem2a  40206  bisaiaisb  43143  confun4  43172  confun5  43173  ichnfim  43618  ichan  43624