Theorem anabs5 375

Description: Absorption into embedded conjunct.

Assertion

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

Proof of Theorem anabs5

Step	Hyp	Ref	Expression
1		ancom 333	. 2 |- (((ph /\ ps) /\ ph) <-> (ph /\ (ph /\ ps)))
2		anabs1 374	. 2 |- (((ph /\ ps) /\ ph) <-> (ph /\ ps))
3	1, 2	bitr3 153	1 |- ((ph /\ (ph /\ ps)) <-> (ph /\ ps))

Syntax hints:   <-> wb 127   /\ wa 196

This theorem is referenced by:  zfrep3 1476

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

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org