Theorem anidmdbi 10427

Description: Conjunct idempotence deduction equivalency. (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 432	. 2 |- ((ps /\ ps) <-> ps)
2	1	imbi2i 185	1 |- ((ph -> (ps /\ ps)) <-> (ph -> ps))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223

This theorem is referenced by:  1ded 10622

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain