Theorem anidmdbi 678

Description: Conjunction idempotence with antecedent. (Contributed by Roy F. Longton, 8-Aug-2005.)

Assertion

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

Proof of Theorem anidmdbi

Step	Hyp	Ref	Expression
1		anidm 676	. 2 |- ( ( ps /\ ps ) <-> ps )
2	1	imbi2i 326	1 |- ( ( ph -> ( ps /\ ps ) ) <-> ( 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:  nanim  1452