Theorem xorbi12d

Description: Equality property for exclusive disjunction. (Contributed by Mario Carneiro, 4-Sep-2016)

	Ref	Expression
Hypotheses	xor12d.1	|- ( ph -> ( ps <-> ch ) )
	xor12d.2	|- ( ph -> ( th <-> ta ) )
Assertion	xorbi12d	|- ( ph -> ( ( ps \/_ th ) <-> ( ch \/_ ta ) ) )

Proof

Step	Hyp	Ref	Expression
1		xor12d.1	|- ( ph -> ( ps <-> ch ) )
2		xor12d.2	|- ( ph -> ( th <-> ta ) )
3	1 2	bibi12d	|- ( ph -> ( ( ps <-> th ) <-> ( ch <-> ta ) ) )
4	3	notbid	|- ( ph -> ( -. ( ps <-> th ) <-> -. ( ch <-> ta ) ) )
5		df-xor	|- ( ( ps \/_ th ) <-> -. ( ps <-> th ) )
6		df-xor	|- ( ( ch \/_ ta ) <-> -. ( ch <-> ta ) )
7	4 5 6	3bitr4g	|- ( ph -> ( ( ps \/_ th ) <-> ( ch \/_ ta ) ) )