Theorem wl-ax11-lem1

Description: A transitive law for variable identifying expressions. (Contributed by Wolf Lammen, 30-Jun-2019)

	Ref	Expression
Assertion	wl-ax11-lem1	|- ( A. x x = y -> ( A. x x = z <-> A. y y = z ) )

Proof

Step	Hyp	Ref	Expression
1		wl-aetr	|- ( A. x x = y -> ( A. x x = z -> A. y y = z ) )
2		wl-aetr	|- ( A. y y = x -> ( A. y y = z -> A. x x = z ) )
3	2	aecoms	|- ( A. x x = y -> ( A. y y = z -> A. x x = z ) )
4	1 3	impbid	|- ( A. x x = y -> ( A. x x = z <-> A. y y = z ) )