Theorem an31 841

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 840	. 2 |- ( ( ph /\ ( ps /\ ch ) ) <-> ( ch /\ ( ps /\ ph ) ) )
2		anass 681	. 2 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
3		anass 681	. 2 |- ( ( ( ch /\ ps ) /\ ph ) <-> ( ch /\ ( ps /\ ph ) ) )
4	1, 2, 3	3bitr4i 292	1 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ch /\ ps ) /\ ph ) )

Syntax hints:   <-> wb 196   /\ wa 384

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 197  df-an 386

This theorem is referenced by:  euind  3393  reuind  3411  dchrelbas3  24963  lhpexle3  35298  4an31  38704  abciffcbatnabciffncba  41096