Theorem bicom1 211

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

Assertion

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

Proof of Theorem bicom1

Step	Hyp	Ref	Expression
1		biimpr 210	. 2 |- ( ( ph <-> ps ) -> ( ps -> ph ) )
2		biimp 205	. 2 |- ( ( ph <-> ps ) -> ( ph -> ps ) )
3	1, 2	impbid 202	1 |- ( ( ph <-> ps ) -> ( ps <-> ph ) )

Syntax hints:   -> wi 4   <-> wb 196

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 197

This theorem is referenced by:  bicom  212  bicomi  214  con3ALT  1032  rp-fakenanass  37860  frege55aid  38159  frege55lem2a  38161  bisaiaisb  41080  confun4  41109  confun5  41110