Theorem and4com 14267

Description: A consequence of /\ associativity in a triple conjunct. (The proof was shortened by Andrew Salmon, 25-May-2011.)

Assertion

Ref	Expression
and4com	|- ((ph /\ (ps /\ ch /\ th)) <-> ((ph /\ ps /\ ch) /\ th))

Proof of Theorem and4com

Step	Hyp	Ref	Expression
1		3anass 862	. . 3 |- ((ps /\ ch /\ th) <-> (ps /\ (ch /\ th)))
2	1	anbi2i 538	. 2 |- ((ph /\ (ps /\ ch /\ th)) <-> (ph /\ (ps /\ (ch /\ th))))
3		3anass 862	. 2 |- ((ph /\ ps /\ (ch /\ th)) <-> (ph /\ (ps /\ (ch /\ th))))
4		and4as 14266	. 2 |- ((ph /\ ps /\ (ch /\ th)) <-> ((ph /\ ps /\ ch) /\ th))
5	2, 3, 4	3bitr2i 196	1 |- ((ph /\ (ps /\ ch /\ th)) <-> ((ph /\ ps /\ ch) /\ th))

Syntax hints:   <-> wb 163   /\ wa 240   /\ w3a 858

This theorem is referenced by:  eeeeanv 14272

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 164  df-an 242  df-3an 860

Copyright terms: Public domain