Theorem bj-sbidmOLD

Description: Obsolete proof of sbidm temporarily kept here to check it gives no additional insight. (Contributed by NM, 8-Mar-1995) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	bj-sbidmOLD	|- ( [ y / x ] [ y / x ] ph <-> [ y / x ] ph )

Proof

Step	Hyp	Ref	Expression
1		equsb2	|- [ y / x ] y = x
2		sbequ12r	|- ( y = x -> ( [ y / x ] ph <-> ph ) )
3	2	sbimi	|- ( [ y / x ] y = x -> [ y / x ] ( [ y / x ] ph <-> ph ) )
4	1 3	ax-mp	|- [ y / x ] ( [ y / x ] ph <-> ph )
5		sbbi	|- ( [ y / x ] ( [ y / x ] ph <-> ph ) <-> ( [ y / x ] [ y / x ] ph <-> [ y / x ] ph ) )
6	4 5	mpbi	|- ( [ y / x ] [ y / x ] ph <-> [ y / x ] ph )