Theorem an31 775

Description: A rearrangement of conjuncts. (Contributed by NM, 24-Jun-2012.) (Proof shortened by Wolf Lammen, 31-Dec-2012.)

Assertion

Ref	Expression
an31	|- (((ph /\ ps) /\ ch) <-> ((ch /\ ps) /\ ph))

Proof of Theorem an31

Step	Hyp	Ref	Expression
1		an13 774	. 2 |- ((ph /\ (ps /\ ch)) <-> (ch /\ (ps /\ ph)))
2		anass 630	. 2 |- (((ph /\ ps) /\ ch) <-> (ph /\ (ps /\ ch)))
3		anass 630	. 2 |- (((ch /\ ps) /\ ph) <-> (ch /\ (ps /\ ph)))
4	1, 2, 3	3bitr4i 268	1 |- (((ph /\ ps) /\ ch) <-> ((ch /\ ps) /\ ph))

Syntax hints:   <-> wb 176   /\ wa 358

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 177  df-an 360

This theorem is referenced by:  euind  3023  reuind  3039