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Theorem ax9v 1914
Description: Weakened version of ax-9 1913, with a dv condition on  x ,  y. This should be the only proof referencing ax-9 1913, and it should be referenced only by its two weakened versions ax9v1 1915 and ax9v2 1916, from which ax-9 1913 is then rederived as ax9 1917, which shows that either ax9v 1914 or the conjunction of ax9v1 1915 and ax9v2 1916 is sufficient. (Contributed by BJ, 7-Dec-2020.) Use ax9 1917 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
StepHypRef Expression
1 ax-9 1913 1  |-  ( x  =  y  ->  (
z  e.  x  -> 
z  e.  y ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-9 1913
This theorem is referenced by:  ax9v1  1915  ax9v2  1916
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