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Axiom ax-nul 3906
Description: The Null Set Axiom of IZF set theory. It was derived as axnul 3905 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 ¬ 𝑦𝑥
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 1435 . . . 4 wff 𝑦𝑥
43wn 3 . . 3 wff ¬ 𝑦𝑥
54, 1wal 1283 . 2 wff 𝑦 ¬ 𝑦𝑥
65, 2wex 1422 1 wff 𝑥𝑦 ¬ 𝑦𝑥
Colors of variables: wff set class
This axiom is referenced by:  0ex  3907  dtruarb  3964
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