Theorem dral1ALT

Description: Alternate proof of dral1 , shorter but requiring ax-11 . (Contributed by NM, 24-Nov-1994) (Proof shortened by Wolf Lammen, 22-Apr-2018) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	dral1.1	|- ( A. x x = y -> ( ph <-> ps ) )
Assertion	dral1ALT	|- ( A. x x = y -> ( A. x ph <-> A. y ps ) )

Proof

Step	Hyp	Ref	Expression
1		dral1.1	|- ( A. x x = y -> ( ph <-> ps ) )
2	1	dral2	|- ( A. x x = y -> ( A. x ph <-> A. x ps ) )
3		axc11	|- ( A. x x = y -> ( A. x ps -> A. y ps ) )
4		axc11r	|- ( A. x x = y -> ( A. y ps -> A. x ps ) )
5	3 4	impbid	|- ( A. x x = y -> ( A. x ps <-> A. y ps ) )
6	2 5	bitrd	|- ( A. x x = y -> ( A. x ph <-> A. y ps ) )