Theorem mojust

Description: Soundness justification theorem for df-mo . (Contributed by NM, 11-Mar-2010) Added this theorem by adapting the proof of eujust . (Revised by BJ, 30-Sep-2022)

	Ref	Expression
Assertion	mojust	|- ( E. y A. x ( ph -> x = y ) <-> E. z A. x ( ph -> x = z ) )

Proof

Step	Hyp	Ref	Expression
1		equequ2	|- ( y = z -> ( x = y <-> x = z ) )
2	1	imbi2d	|- ( y = z -> ( ( ph -> x = y ) <-> ( ph -> x = z ) ) )
3	2	albidv	|- ( y = z -> ( A. x ( ph -> x = y ) <-> A. x ( ph -> x = z ) ) )
4	3	cbvexvw	|- ( E. y A. x ( ph -> x = y ) <-> E. z A. x ( ph -> x = z ) )