Theorem an21 471

Description: Swap two conjuncts. (Contributed by Peter Mazsa, 18-Sep-2022.)

Assertion

Ref	Expression
an21	|- ( ( ( ph /\ ps ) /\ ch ) <-> ( ps /\ ( ph /\ ch ) ) )

Proof of Theorem an21

Step	Hyp	Ref	Expression
1		biid 171	. . 3 |- ( ( ph /\ ch ) <-> ( ph /\ ch ) )
2	1	bianassc 470	. 2 |- ( ( ps /\ ( ph /\ ch ) ) <-> ( ( ph /\ ps ) /\ ch ) )
3	2	bicomi 132	1 |- ( ( ( ph /\ ps ) /\ ch ) <-> ( ps /\ ( ph /\ 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:  imasabl  13542