Theorem bicom1 210

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 209	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜓 → 𝜑))
2		biimp 204	. 2 ⊢ ((𝜑 ↔ 𝜓) → (𝜑 → 𝜓))
3	1, 2	impbid 201	1 ⊢ ((𝜑 ↔ 𝜓) → (𝜓 ↔ 𝜑))

Syntax hints:   → wi 4   ↔ wb 195

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 196

This theorem is referenced by:  bicom  211  bicomi  213  con3ALT  1026  rp-fakenanass  36879  frege55aid  37179  frege55lem2a  37181  bisaiaisb  39729  confun4  39758  confun5  39759