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Axiom ax-nul 5196
Description: The Null Set Axiom of ZF set theory. It was derived as axnul 5195 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 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 2116 . . . 4 wff 𝑦𝑥
43wn 3 . . 3 wff ¬ 𝑦𝑥
54, 1wal 1536 . 2 wff 𝑦 ¬ 𝑦𝑥
65, 2wex 1781 1 wff 𝑥𝑦 ¬ 𝑦𝑥
Colors of variables: wff setvar class
This axiom is referenced by:  0ex  5197  dtru  5258  axprlem1  5311  axprlem4  5314  axprlem5  5315  bj-dtru  34201  sn-dtru  39342  eu0  40148
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