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Axiom ax-nul 4165
Description: The Null Set Axiom of ZF set theory. It was derived as axnul 4164 above and is therefore redundant, but we state it as a separate axiom here so that its uses can be identified more easily. (Contributed by NM, 7-Aug-2003.)
Assertion
Ref Expression
ax-nul  |-  E. x A. y  -.  y  e.  x
Distinct variable group:    x, y

Detailed syntax breakdown of Axiom ax-nul
StepHypRef Expression
1 vy . . . . 5  set  y
2 vx . . . . 5  set  x
31, 2wel 1697 . . . 4  wff  y  e.  x
43wn 3 . . 3  wff  -.  y  e.  x
54, 1wal 1530 . 2  wff  A. y  -.  y  e.  x
65, 2wex 1531 1  wff  E. x A. y  -.  y  e.  x
Colors of variables: wff set class
This axiom is referenced by:  0ex  4166  dtru  4217
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