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Mirrors > Home > MPE Home > Th. List > 0ex | Structured version Visualization version Unicode version |
Description: The Null Set Axiom of ZF set theory: the empty set exists. Corollary 5.16 of [TakeutiZaring] p. 20. For the unabbreviated version, see ax-nul 4548. (Contributed by NM, 21-Jun-1993.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
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0ex |
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Step | Hyp | Ref | Expression |
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1 | ax-nul 4548 |
. . 3
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2 | eq0 3759 |
. . . 4
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3 | 2 | exbii 1729 |
. . 3
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4 | 1, 3 | mpbir 214 |
. 2
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5 | 4 | issetri 3064 |
1
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