Theorem bj-bixor

Description: Equivalence of two ternary operations. Note the identical order and parenthesizing of the three arguments in both expressions. (Contributed by BJ, 31-Dec-2023)

	Ref	Expression
Assertion	bj-bixor	|- ( ( ph <-> ( ps \/_ ch ) ) <-> ( ph \/_ ( ps <-> ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm5.18	|- ( ( ph <-> ( ps <-> ch ) ) <-> -. ( ph <-> -. ( ps <-> ch ) ) )
2	1	con2bii	|- ( ( ph <-> -. ( ps <-> ch ) ) <-> -. ( ph <-> ( ps <-> ch ) ) )
3		df-xor	|- ( ( ps \/_ ch ) <-> -. ( ps <-> ch ) )
4	3	bibi2i	|- ( ( ph <-> ( ps \/_ ch ) ) <-> ( ph <-> -. ( ps <-> ch ) ) )
5		df-xor	|- ( ( ph \/_ ( ps <-> ch ) ) <-> -. ( ph <-> ( ps <-> ch ) ) )
6	2 4 5	3bitr4i	|- ( ( ph <-> ( ps \/_ ch ) ) <-> ( ph \/_ ( ps <-> ch ) ) )