Theorem cbveuwOLD

Description: Obsolete version of cbveuw as of 23-May-2024. (Contributed by NM, 25-Nov-1994) (Revised by Gino Giotto, 10-Jan-2024) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	cbveuwOLD.1	|- F/ y ph
	cbveuwOLD.2	|- F/ x ps
	cbveuwOLD.3	|- ( x = y -> ( ph <-> ps ) )
Assertion	cbveuwOLD	|- ( E! x ph <-> E! y ps )

Proof

Step	Hyp	Ref	Expression
1		cbveuwOLD.1	|- F/ y ph
2		cbveuwOLD.2	|- F/ x ps
3		cbveuwOLD.3	|- ( x = y -> ( ph <-> ps ) )
4	1	sb8euv	|- ( E! x ph <-> E! y [ y / x ] ph )
5	2 3	sbiev	|- ( [ y / x ] ph <-> ps )
6	5	eubii	|- ( E! y [ y / x ] ph <-> E! y ps )
7	4 6	bitri	|- ( E! x ph <-> E! y ps )