Theorem wl-lem-exsb

Description: This theorem provides a basic working step in proving theorems about E* or E! . (Contributed by Wolf Lammen, 3-Oct-2019)

	Ref	Expression
Assertion	wl-lem-exsb	|- ( x = y -> ( ph <-> A. x ( x = y -> ph ) ) )

Proof

Step	Hyp	Ref	Expression
1		ax12v2	|- ( x = y -> ( ph -> A. x ( x = y -> ph ) ) )
2		sp	|- ( A. x ( x = y -> ph ) -> ( x = y -> ph ) )
3	2	com12	|- ( x = y -> ( A. x ( x = y -> ph ) -> ph ) )
4	1 3	impbid	|- ( x = y -> ( ph <-> A. x ( x = y -> ph ) ) )