Theorem bicom1 190

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

Assertion

Ref	Expression
bicom1	|- ((ph <-> ps) -> (ps <-> ph))

Proof of Theorem bicom1

Step	Hyp	Ref	Expression
1		bi2 189	. 2 |- ((ph <-> ps) -> (ps -> ph))
2		bi1 178	. 2 |- ((ph <-> ps) -> (ph -> ps))
3	1, 2	impbid 183	1 |- ((ph <-> ps) -> (ps <-> ph))

Syntax hints:   -> wi 4   <-> wb 176

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 177

This theorem is referenced by:  bicom  191  bicomi  193