Theorem aaanOLD

Description: Obsolete version of aaan as of 21-Nov-2024. (Contributed by NM, 12-Aug-1993) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	aaan.1	|- F/ y ph
	aaan.2	|- F/ x ps
Assertion	aaanOLD	|- ( A. x A. y ( ph /\ ps ) <-> ( A. x ph /\ A. y ps ) )

Proof

Step	Hyp	Ref	Expression
1		aaan.1	|- F/ y ph
2		aaan.2	|- F/ x ps
3	1	19.28	|- ( A. y ( ph /\ ps ) <-> ( ph /\ A. y ps ) )
4	3	albii	|- ( A. x A. y ( ph /\ ps ) <-> A. x ( ph /\ A. y ps ) )
5	2	nfal	|- F/ x A. y ps
6	5	19.27	|- ( A. x ( ph /\ A. y ps ) <-> ( A. x ph /\ A. y ps ) )
7	4 6	bitri	|- ( A. x A. y ( ph /\ ps ) <-> ( A. x ph /\ A. y ps ) )