Theorem ax9v 2000

Description: Weakened version of ax-9 1999, with a dv condition on x , y. This should be the only proof referencing ax-9 1999, and it should be referenced only by its two weakened versions ax9v1 2001 and ax9v2 2002, from which ax-9 1999 is then rederived as ax9 2003, which shows that either ax9v 2000 or the conjunction of ax9v1 2001 and ax9v2 2002 is sufficient. (Contributed by BJ, 7-Dec-2020.) Use ax9 2003 instead. (New usage is discouraged.)

Assertion

Ref	Expression
ax9v	|- ( x = y -> ( z e. x -> z e. y ) )

Distinct variable group:   x, y

Proof of Theorem ax9v

Step	Hyp	Ref	Expression
1		ax-9 1999	1 |- ( x = y -> ( z e. x -> z e. y ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-9 1999

This theorem is referenced by:  ax9v1  2001  ax9v2  2002