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Axiom ax-nul 3874
Description: The Null Set Axiom of IZF set theory. It was derived as axnul 3873 above and is therefore redundant, but we state it as a separate axiom here so that its uses can be identified more easily. Axiom 4 of [Crosilla] p. "Axioms of CZF and IZF". (Contributed by NM, 7-Aug-2003.)
Assertion
Ref Expression
ax-nul xy ¬ y x
Distinct variable group:   x,y

Detailed syntax breakdown of Axiom ax-nul
StepHypRef Expression
1 vy . . . . 5 setvar y
2 vx . . . . 5 setvar x
31, 2wel 1391 . . . 4 wff y x
43wn 3 . . 3 wff ¬ y x
54, 1wal 1240 . 2 wff y ¬ y x
65, 2wex 1378 1 wff xy ¬ y x
Colors of variables: wff set class
This axiom is referenced by:  0ex  3875  dtruarb  3933
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