Theorem biimt 325

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 35	. 2 |- (ph -> ((ph -> ps) -> ps))
3	1, 2	impbid2 195	1 |- (ph -> (ps <-> (ph -> ps)))

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:  pm5.5  326  a1bi  327  mtt  329  abai  770  dedlem0a  918  ceqsralt  2882  reu8  3032  csbiebt  3172  r19.3rz  3641  r19.3rzv  3643  ralidm  3653  fncnv  5158