Theorem biimt 240

Description: A wff is equivalent to itself with true antecedent. (Contributed by NM, 28-Jan-1996.)

Assertion

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

Proof of Theorem biimt

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 |- ( ps -> ( ph -> ps ) )
2		pm2.27 40	. 2 |- ( ph -> ( ( ph -> ps ) -> ps ) )
3	1, 2	impbid2 142	1 |- ( ph -> ( ps <-> ( ph -> ps ) ) )

Syntax hints:   -> wi 4   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm5.5  241  a1bi  242  abai  555  dedlem0a  963  ceqsralt  2757  reu8  2926  csbiebt  3088  r19.3rm  3503  fncnv  5264  ovmpodxf  5978  brecop  6603  tgss2  12873