Theorem bi3 112

Description: Property of the biconditional connective. (Contributed by NM, 11-May-1999.)

Assertion

Ref	Expression
bi3	|- ( ( ph -> ps ) -> ( ( ps -> ph ) -> ( ph <-> ps ) ) )

Proof of Theorem bi3

Step	Hyp	Ref	Expression
1		df-bi 110	. . 3 |- ( ( ( ph <-> ps ) -> ( ( ph -> ps ) /\ ( ps -> ph ) ) ) /\ ( ( ( ph -> ps ) /\ ( ps -> ph ) ) -> ( ph <-> ps ) ) )
2	1	simpri 106	. 2 |- ( ( ( ph -> ps ) /\ ( ps -> ph ) ) -> ( ph <-> ps ) )
3	2	ex 108	1 |- ( ( ph -> ps ) -> ( ( ps -> ph ) -> ( ph <-> ps ) ) )

Syntax hints:   -> wi 4   /\ wa 97   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  impbii  117  impbidd  118  bisym  214