Theorem birot

Description: Rotation of the arguments of the nested implication ( . <-> ( . <-> . ) ) (a general phenomenon for a commutative associative binary operation, see e.g., inrot ) . (Contributed by BJ, 10-Aug-2026)

	Ref	Expression
Assertion	birot	|- ( ( ph <-> ( ps <-> ch ) ) <-> ( ps <-> ( ch <-> ph ) ) )

Proof

Step	Hyp	Ref	Expression
1		bicom	|- ( ( ph <-> ( ps <-> ch ) ) <-> ( ( ps <-> ch ) <-> ph ) )
2		biass	|- ( ( ( ps <-> ch ) <-> ph ) <-> ( ps <-> ( ch <-> ph ) ) )
3	1 2	bitri	|- ( ( ph <-> ( ps <-> ch ) ) <-> ( ps <-> ( ch <-> ph ) ) )