Theorem an31 498

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 497	. 2 |- ( ( ph /\ ( ps /\ ch ) ) <-> ( ch /\ ( ps /\ ph ) ) )
2		anass 381	. 2 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
3		anass 381	. 2 |- ( ( ( ch /\ ps ) /\ ph ) <-> ( ch /\ ( ps /\ ph ) ) )
4	1, 2, 3	3bitr4i 201	1 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ch /\ ps ) /\ ph ) )

Syntax hints:   /\ wa 97   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  euind  2728  reuind  2744