Theorem aibandbiaiaiffb 41062

Description: A closed form showing (a implies b and b implies a) implies (a same-as b). (Contributed by Jarvin Udandy, 3-Sep-2016.)

Assertion

Ref	Expression
aibandbiaiaiffb	|- ( ( ( ph -> ps ) /\ ( ps -> ph ) ) -> ( ph <-> ps ) )

Proof of Theorem aibandbiaiaiffb

Step	Hyp	Ref	Expression
1		dfbi2 660	. 2 |- ( ( ph <-> ps ) <-> ( ( ph -> ps ) /\ ( ps -> ph ) ) )
2	1	biimpri 218	1 |- ( ( ( ph -> ps ) /\ ( ps -> ph ) ) -> ( ph <-> ps ) )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384

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  df-an 386

This theorem is referenced by: (None)