Theorem an43 588

Description: Rearrangement of 4 conjuncts. (Contributed by Rodolfo Medina, 24-Sep-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)

Assertion

Ref	Expression
an43	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ th ) /\ ( ps /\ ch ) ) )

Proof of Theorem an43

Step	Hyp	Ref	Expression
1		an42 587	. 2 |- ( ( ( ph /\ th ) /\ ( ps /\ ch ) ) <-> ( ( ph /\ ps ) /\ ( ch /\ th ) ) )
2	1	bicomi 132	1 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ph /\ th ) /\ ( ps /\ ch ) ) )

Syntax hints:   /\ wa 104   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  an3  589