Theorem anabs5 784

Description: Absorption into embedded conjunct. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 9-Dec-2012.)

Assertion

Ref	Expression
anabs5	|- ((ph /\ (ph /\ ps)) <-> (ph /\ ps))

Proof of Theorem anabs5

Step	Hyp	Ref	Expression
1		ibar 490	. . 3 |- (ph -> (ps <-> (ph /\ ps)))
2	1	bicomd 192	. 2 |- (ph -> ((ph /\ ps) <-> ps))
3	2	pm5.32i 618	1 |- ((ph /\ (ph /\ ps)) <-> (ph /\ ps))

This proof depends on syntax axioms:   <-> wb 176   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by: (None)