Theorem xorbi12i

Description: Equality property for exclusive disjunction. (Contributed by Mario Carneiro, 4-Sep-2016) (Proof shortened by Wolf Lammen, 21-Apr-2024)

	Ref	Expression
Hypotheses	xorbi12.1	|- ( ph <-> ps )
	xorbi12.2	|- ( ch <-> th )
Assertion	xorbi12i	|- ( ( ph \/_ ch ) <-> ( ps \/_ th ) )

Proof

Step	Hyp	Ref	Expression
1		xorbi12.1	|- ( ph <-> ps )
2		xorbi12.2	|- ( ch <-> th )
3		df-xor	|- ( ( ph \/_ ch ) <-> -. ( ph <-> ch ) )
4	1 2	bibi12i	|- ( ( ph <-> ch ) <-> ( ps <-> th ) )
5	3 4	xchbinx	|- ( ( ph \/_ ch ) <-> -. ( ps <-> th ) )
6		df-xor	|- ( ( ps \/_ th ) <-> -. ( ps <-> th ) )
7	5 6	bitr4i	|- ( ( ph \/_ ch ) <-> ( ps \/_ th ) )